A number not always represent the same thing, therefore 1 not always equal 1.
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after 5 votes the winner is...
GorefordMaximillion
Voting Style:  Open  Point System:  7 Point  
Started:  11/27/2012  Category:  Miscellaneous  
Updated:  4 years ago  Status:  Post Voting Period  
Viewed:  2,332 times  Debate No:  27570 
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As requested by my opponent, I should give this another try.
"Rules: First round: is acceptance Second round: I will present my argument, and CON will present his, which should contradict my, meaning he should demonstrate that 1 always hold the same value, and will always equal 1. 1 should always represent 1. Third round: Both, CON and I, will exam each others presentation and point any flaws in reason, and reason only, if there is any. Fourth round: Both can attempt to negate the flaws suggested in the previous round. To make it simple, you may only use numbers and only use the four basic operators (plus, minus, divide, multiply). There should be no sources but your mind. Nothing in this initial statement should need to be defined."
I accept and thank you for the challenge! I've been waiting for this since I read your original debate on it!!! 

I thank CON for accepting and requesting this debate, and hope I can finally advance anywhere this time.
My last opponent seems to have missed my concept because of the word "object", and him as well as my first opponent believed that by adding the two fractions, it was an accepted way to show how 1/2 / 1/2 was equal to 1, and prove my statement wrong. I will try to rewrite my original statement in a different way, and at the same time go over these point, of which is very flawed. Demonstration. 1/2 / 1/2= 1 1+0= 1 Half goes into half 1 time. The result 1 is the result of how many times 1/2 went into 1/2. I'll demonstrate exactly of why it is how many times. It is "true" that by adding two halves you get the result of one. *Although I also disagreed that two halves is exactly like one, I won't go that far in this debate, and just concentrate on the resolution*. So for the sake of the continuity, I will "accept" that adding two halves is equal to one. It is a coincidence that 1/2 + 1/2 is equal to the same number as 1/2 / 1/2. The reason I chose 1/2 / 1/2 is because it demonstrates that by dividing two numbers, the result is how many times you "divide" that number, and not really anything you are dividing with. Take 4 divided by 2 as an example. When you first learn this, your teacher probably gave you an explanation similar to this; "If I had 4 apples and had to share with 2 kids, how many apples would each get?" Notice, apple and kids are two different things, why is that? Is because it wouldn't work otherwise, you cannot divide 4 apples into 2 apples, is not possible. You could think you could share 4 apples with 2 apples, and this may seem like it would work. Let's try. Imagine 4 apples, and another 2 apples in different places, you like to join those 4 apples to the 2 separated apples equally, you send two apples to each apple. To have the right result, you will have to only consider the 2 apples that you sent to each apple, as if you add the 2 apples to that 1 apple that you had as a separation of the 2 apples, you would count 3 apples, and that wouldn't match the result. Just like that, you will notice adding won't work in this example, so in the example 1/2 / 1/2, adding should not be consider. But wait, what did I just do? I show that the result of 2 wasn't a result of how many times it was divided, but actual apples. OH no, is this debate over? Well, this is precisely why I use 1/2 / 1/2 as an example. Let's imagine the same as we did with 4/2, but this time using 1/2 / 1/2. Imagine 1/2 of an apple. Another1/2 of an apple awaits to be equally dived. I send 1/2 of an apple to the other 1/2 of an apple. That half apple now has half of an apple, the result is 1, the only way I can get 1 apple is if I join them (which is the mistake of my last opponents), but wait, when I did 4/2 I show that adding cannot work. Oh no, we have a contradiction, ok I guess this debate is pointless, and it should end in a tie. Remember what I stated? That division gives you the result of how many times did you divide whatever you had with whatever it is? Let's see if we gain the same result, if I go by what I first stated. 4/2=2 The two in this equation is a container, the 4 is whatever you are dividing into the container. I have 4 apples, I have a container that holds 2 apples, how many times can this container be filled to the limit? 2 times correct? But remember, in the last example I split 2 (since by the teacher's example, we had two kids, which is two separated entities). So let's do the same, for sake of clarity. I have 4 apples, I have 2 container, each of which holds 1 apple (since I split the containers into two), how many times will I fill each container if I dived the apples equally? 2 correct? Let's do the same with 1/2 / 1/2. I have 1/2 of an apple. I have a container that holds 1/2 of an apple. How many times will I be able to fill such of container? Once right? So 1 time. As we see, by this method, both times we active the results that we wanted, and we could only accomplish by counting on how many times did we divide, or fill the container with what we had. 1 with the addition of 0 remains 1. 1 here is a quantity, which remains the same. If I had 1 apple and I added nothing else in addition, I would just have that same apple. The same apple would be the same 1 apple as before. The numeric 1 from 1 apple does not equal the numeric 1 that you get by how many times 1/2 apple can be inserted in a container that holds 1/2. Therefore 1/2 / 1/2 (which equals 1)==1+0(which also equals 1) Therefore 1 does not represent the same 1, which results in 1==1. I hope I was more clear this time around. I now await my opponent.
I will start with the definition of what a number is: A number is a mathematical object used to count, label, and measure. This is from Wikipedia, but I am sure pro will agree with this definition of number. Pro has made a good point in showing that an apple, a child and anything else a number represents is not the same thing. This would be correct. However, a key distinction is being missed. If pro picks up an apple from his kitchen table, how many "1"s" is he holding? He is not holding any "1"s," he is holding 1 apple. The "1" is only representing the quantity of apples he is holding in his hand. If he picks up a knife with his other hand, and then grabs a napkin with the same hand, how many 2"s is he holding in his other hand? He"s not holding any "2"s." He is holding 2 objects. He is also holding 1 knife and 1 napkin. Again, the numbers are not physical things he is holding, but rather mathematical objects used to represent the quantity of the things he is holding. Is 1 apple equal to 1 knife? No, of course not. Is the quantity of apples equal to the quantity of knives? Yes. There is one of each. The quantity is the same" 1 = 1. Pro makes a valid mathematical example in his argument: "1/2 / 1/2= 1 1+0= 1" etc. But next, pro advances arguments that do not use math properly to show what is happening. As a matter of fact, once units are introduced to the math, all of pros examples can be shown to make physical sense. However, his basic argument will still be shown to be wrong. Using units 1 = 1. 1 apple =/= 1 knife. But pro has not made the argument that "1 apple =/= 1 knife." There"s no disagreement there at all. Pro has made the argument that since "1 apple =/= 1 knife," then "1 =/= 1" But the units have changed with the new declaration. A more accurate statement from pro"s example would be "the quantity (1) of apples is equal to the quantity (1) of knives." This is a true statement. There is one of each thing. They are not the same thing. But their quantities are equal to each other" 1 = 1. Pro"s next argument: "Imagine 4 apples, and another 2 apples in different places, you like to join those 4 apples to the 2 separated apples equally, you send two apples to each apple. To have the right result, you will have to only consider the 2 apples that you sent to each apple, as if you add the 2 apples to that 1 apple that you had as a separation of the 2 apples, you would count 3 apples, and that wouldn't match the result. Just like that, you will notice adding won't work in this example, so in the example 1/2 / 1/2, adding should not be consider. But wait, what did I just do? I show that the result of 2 wasn't a result of how many times it was divided, but actual apples. OH no, is this debate over?" In this example, you have incorrectly used math to describe what has happened: "Imagine 4 apples, and another 2 apples in different places, you like to join those 4 apples to the 2 separated apples equally, you send two apples to each apple." There is one math problem there, and it has the correct result also. Why did you send 2 apples to each apple? Because: 4 / 2 = 2. When you add units it makes more sense: 4 apples / 2 apples = 2 apples/apple. Here is how this equation would be read: "4 apples, divided by/amongst 2 apples equals 2 apples per apple." Each apple in the group of two, receives 2 apples from the group of 4. This equation has not addressed adding the apples or joining them. It has only solved how many from the group of 4 you send to each apple in the group of 2. "To have the right result, you will have to only consider the 2 apples that you sent to each apple, as if you add the 2 apples to that 1 apple that you had as a separation of the 2 apples, you would count 3 apples, and that wouldn't match the result." The 3 apples you have mentioned here are a new mathematical equation: "2 apples + 1 apple = 3 apples." This new equation represents "adding" the 2 apples from the group of 4 with the 1 apple from the group of 2. The two equations represent the two things you have done in your example: Dividing up the 4 apples equally amongst two apples, and then adding those 2 apples to the 1 apple. Moving to pro"s next argument: "Imagine 1/2 of an apple. Another1/2 of an apple awaits to be equally dived. I send 1/2 of an apple to the other 1/2 of an apple. That half apple now has half of an apple, the result is 1, the only way I can get 1 apple is if I join them (which is the mistake of my last opponents), but wait, when I did 4/2 I show that adding cannot work. Oh no, we have a contradiction, ok I guess this debate is pointless, and it should end in a tie." By "sending" the half of the apple to the other half of an apple you get the correct mathematical result when the units are set up properly: "1 (1/2 of an apple) / 1 (1/2 of an apple) = 1 (1/2 of an apple)/(1/2 of an apple)" It is this equation that represent how to divide, or divvy up evenly, " of an apple to " of an apple. This equation also works: "" apple / " apple = 1 apple/apple" This is a rate which also applies. For every 1 apple I have, I send 1 apple to it. Next, you join them: "1/2 apple + " apple = 1 apple" You would agree this is correct right? "That division gives you the result of how many times did you divide whatever you had with whatever it is?" What the math problem represents all depends on the units and how the math problem is set up. "4/2=2 The two in this equation is a container, the 4 is whatever you are dividing into the container." I have 4 apples, I have a container that holds 2 apples, how many times can this container be filled to the limit? 2 times correct?" So, to properly set up this equation using units (we will use apples going into the container): "4 apples / 2 containers = 2 apples / container" Or "4 apples divided into two containers equals 2 apples per container" The equation you used is correct, I have merely added units to clarify. "I have 4 apples, I have 2 container, each of which holds 1 apple (since I split the containers into two), how many times will I fill each container if I dived the apples equally? 2 correct?" Again, this is two problems: "4 apples / 2 containers = 2 apples / container" Remember, all this is saying is that to evenly divide the 4 apples into the 2 containers, you take 2 of the four apples to each container. It says nothing about putting the apples into the container, nor the quantity of apples the container can hold. And, for one container, since it can only hold 1 apple, but I have 2 apples to go into it: "1 / 2 = 1 remainder 1." (not "one half" but one divided by 2) You can put in one apple and you have one apple left (the remainder) you cannot put in. Even equating the problem to one half, you can put half of your 2 apples into the container. "The numeric 1 from 1 apple does not equal the numeric 1 that you get by how many times 1/2 apple can be inserted in a container that holds 1/2." Again, the numeric 1 does because the numeric 1 is only representing a quantity of things, not the actual things. I hope I have explained things thoroughly enough for my opponent! I look forward to your response! 

I accept the number definition, as I cannot think of a better one. I only brought out apples and kids as a demonstration of how we were thought, and how wrong that could be. I proceeded to only use one type of object for this reason, to not confuse my argument to be; that if you had 1 to represent apple in one side, and 1 on the other side to represent knife (as my opponent pointed), 1 and 1 wouldn't be equals since apple and knife aren't the same. Like my opponent pointed, apples and knives are both quantities of an object, so the number 1's would be equal to quantity of objects. Therefore, I'm in agreement with this, and is not part of my argument. My point is, can division give the result of anything but, of how many times did you divide? Can division give you the result of quantity of objects? If it can be done, there must be a way to show this being done, with whole numbers as well as fractions, with the same rules. If by having 4/2 I count 2 of the result as being a quantity of an object, then if I have 1/2 / 1/2, I should also be able to count the end result as a quantity of an object. So please show me, how do I get 1 object if I have 1/2 object divided by 1/2 object. How about 1/4 / 1/4, which is also 1, but unlike 1/2 / 1/2 adding won't work. I notice your use of; "pro advances arguments that do not use math properly to show what is happening", and other places you also call my methods to not use mathematics properly, even know I active the same result by my method. *remember I'm accusing math to be flawed, not that I believe to be right, just that is how I'm seeing at the moment, so my demonstration was an alternative way to do math; by using the dividend as the object being divided (of which I use an apple), and the divisor as a container. By doing so, I showed I can always active the same result, using the same method, with both whole numbers and fractions. This is also the reason of why I said you must show flaws in reason, and in reason only, and not in mathematical statement since if I'm right that there is a flaw in mathematics (which I hope to be wrong), using a flaw argument to prove a flaw cannot work. Therefore, the rules of mathematics is into question. CON wrote; PRO questions; Do you mean, one 1/2 of an apple divided by one 1/2 of an apple? It feels very confusing. 1/2 is a unit in itself, just like 1 is just 1 unit, but 1/2 is not the same as 1. You use addition to obtain 1 apple here, but yet with whole numbers you never use any addition to demonstrate the same thing. Can you show me this same example using 1/4 / 1/4 and 4/2? I try to demonstrate that using addition doesn't work, as you cannot do the same with whole numbers, but perhaps you believe it can be done, of which why you ignored what I said and attempted to demonstrate that adding was plausible. CON wrote; PRO questions; Why did you feel my statement was incorrect? What is the math problem that you see? You feel there is a problem, but the result is the same. It looks like you can see from my point of view now. You see an incorrect statement, but a correct result. This means that, just because result remains the same, it doesn't mean something was done properly, just like I still don't understand why one would correlate 1/2 / 1/2 and 1/2 + 1/2. Now you feel my pain. Why did I send the 2 apples to each apple you ask? Remember, I said 1 and 1/2 is one set, but 2 isn't. To divide 4 equally into 2, I must take this into account. If I count 2 as just 1 set, I will just send the 4 apples to that set, and the result would be 4 and not 2. So if I had 4 apples, and I just send to 2 apples, that would show the 2 apples being part of the same set, and all 4 apples would end in the same place. The 2 apples must act as two different sets to active the result desire. On the method I presented, this does not need to happen, since 2 is a quantity that the container holds, so I can split the container into two sets if I like, or I can just send the apples to the 1 container and count how many times I was able to fill it up. In both ways the result remain the same. I do not get your use of grouping, by saying group of two you count 2 as being just 1 set. So to make clear and simply, what I'm saying from my resolution is. Use "apples" to start from the equation 1+01/2 / 1/2, use "apples" to start the equation <<(1/2 / 1/2). From what I see; from one side you start with apples and ends with apples represented by 1(which is one whole apple), on the other side because of division, you start with apples, but the result is not apples, so 1 does not represent 1 apple. Of why 1+0==1/ / 1/2. I see the end result being how many times you divide, so I see 1 as being, 1 (whole) time. I cannot see how you can get 1 whole apple out of this. So all you got to do, is show me, how exactly do you get half of an apple to be divided by half of an apple and get the result of 1 in apples? If you want to continue to show me this by adding, then also do it using 1/4 / 1/4. Therefore, the only time I see 1 not equal to 1 is when you have an equation using the operation of division that equals to 1 in one side, and on the other side any of the other basic operations to also equal 1. I feel that both 1's from both sides cannot be equal since they represent different things. So basically division is not comparable with the other operations since they cannot active the same purposes. So it goes beyond 1==1, of why I told you, I need you to prove me wrong. Conclusion. By going point by point, my opponent missed my reasoning, and have of his round was filled with misinterpretation of what I was trying to convey, and assume something that in the begin of this round I state to be completely untrue. By going point by point, my opponent missed that half of my previous round, as I was just trying to demonstrate that, by going by what such of teacher would say, it was unreasonable to use two exactly objects. I showed that by trying to follow such of reason, and point to the problem in the end. If my opponent saw such of flaw in reason in the begin half of my second round, then this proves he sees that by going by the teachings of a teacher, such of argument as using the same object for both the quotient and the divisor won't work. Therefore, the quotient and the divisor cannot represent the same thing. By going point by point, and missing what I did in the beginning, my opponent just use that same argument as I previously show not to work. I would ask my opponent to re read my second round again, and try to address those mistakes, and take my second round as just one whole point, instead of assuming there are many points I was trying to make. Sure there are many points, but all those points are to try to make you see my initial point, and not per se to be taken as many points. So read it completely, if you then find that because of one of my points my reason was wrong, then you could rewrite my argument in the same fashion, but fixing my mistake, which should show along the way that it was a mistake. Kind of like I did, by starting to something I did not agreed with, just to show how it wouldn't work. Since you made those mistakes, attempting to go point by point in this round was just an attempt to show you those mistakes, and since they were made, it was really confusing to follow. So before "Conclusion", my round may even look like an off topic reply, but I was just trying to understand your reasoning, and give you more information behind my.
I only brought out apples and kids as a demonstration of how we were thought, and how wrong that could be." I recall you telling me English was your 2nd language, so can I assume you mean "taught?" There are several other grammatical errors, which I do not hold against you. However I am forced to make reasonable assumptions as to what you have meant. "My point is, can division give the result of anything but, of how many times did you divide? Can division.... with the same rules." Maybe I missed the point of this debate and your argument then? I tried to show you the flaw of your arguments, point by point, as you made them. Also, I went chronologically, point by point, to maintain a coherent flow to the discussion. "If by having 4/2 I count 2 of the result as being a quantity of an object, then if I .... adding won't work." Two examples: I have two groups of apples (group A and B). In each group, there is half an apple. I want to figure out how many apples from group A to send to group B. In other words, I want to "divide" my group A members evenly among my group B members. My answer will be: 1/2 apple / 1/2 apple = 1 apple/apple. I have a rate. For every apple in group B, I send an apple from group A to it. The rate would be the same with group A and B each having 1/4 an apple in the group: 1/4 apple / 1/4 apple = 1 apple/apple. Again, for every apple in group B, I send an apple from group A. Since I have 1/2 an apple in group B, and I must maintain that rate, I send 1/2 an apple from group A. So, in summary, the 1 object (in my example, apple) you get is the number of apples in group A you send per apple in Group B. "I notice your use of; "pro advances arguments that do not use math properly to show what is happening", and other places you also call my methods to not use mathematics properly, even know I active the same result by my method. *remember I'm accusing math to be flawed, ....This is also the reason of why I said you must show flaws in reason, and in reason only, and not in mathematical statement since if I'm right that there is a flaw in mathematics .... Therefore, the rules of mathematics is into question." I had to point this out because the math was not flawed; rather it was your interpretation and application of it" the "reasoning" of your approach. This is also why I went point by point. I had to show the exact flaws you were making when setting up your equations, which then resulted in a flaw in reason" It was your premise that was incorrect, leading to an incorrect conclusion based on a faulty premise. This is why I believe I have showed your flaw in reasoning. You have set up incorrect mathematical statements to frame your argument. The reasoning behind the mathematical statements you set up was wrong. I then set up the proper mathematical statements to show you the proper reasoning which led to the proper result. "Do you mean, one 1/2 of an apple divided by one 1/2 of an apple? It feels very confusing." Yes. I pasted my argument from Microsoft Word directly into DDO and it resulted in formatting errors. My apologies. Here is the correction: "By "sending" the half of the apple to the other half of an apple you get the correct mathematical result when the units are set up properly: "1 (1/2 of an apple) / 1 (1/2 of an apple) = 1 (1/2 of an apple)/(1/2 of an apple)" It is this equation that represent how to divide, or divvy up evenly, 1/2 of an apple to 1/2 of an apple. This equation also works: "1/2 apple / 1/2 apple = 1 apple/apple" This is a rate which also applies. For every 1 apple I have, I send 1 apple to it. Next, you join them: "1/2 apple + 1/2 apple = 1 apple"" "1/2 is a unit in itself, just like 1 is just 1 unit, but 1/2 is not the same as 1." You use addition to obtain 1 apple here, but yet with whole numbers you never use any addition to demonstrate the same thing. Can you show me this same example using 1/4 / 1/4 and 4/2?"" You can set up the equation both ways and it will still work because 1, 1/2 of an apple is the same as 1/2 of an apple. With the 1/4 apples, the RATE will be the same: 1/4 apple / 1/4 apple = 1 apple/apple When you apply that rate to your 1/4 apples, you send and equal amount of apples for every apple in group b. A 1 to 1 ratio. The process is the same for the 4/2. "Why did you feel my statement was incorrect? What is the math problem that you see? You feel.... Now you feel my pain." Hopefully my past examples have shown how your statements were incorrect. The fact that 1/2 / 1/2 is the same as 1/2 + 1/2 is a coincidence. "I do not get your use of grouping, by saying group of two you count 2 as being just 1 set." Hopefully, using group A and B clarifies this. "I see the end result being how many times you divide, so I see 1 as being, 1 (whole) time. I cannot see how you can get 1 whole apple out of this. So all you got to do, is show me, how exactly do you get half of an apple to be divided by half of an apple and get the result of 1 in apples? If you want to continue to show me this by adding, then also do it using 1/4 / 1/4." Again, the math here gives a rate. Watch the units and observe my previous examples. "Therefore, the only time I see 1 not equal to 1 is when you have an equation using the operation of division that equals to 1 in one side, and on the other side any of the other basic operations to also equal 1. I feel that both 1's from both sides cannot be equal since they represent different things. So basically division is not comparable with the other operations since they cannot active the same purposes. So it goes beyond 1==1, of why I told you, I need you to prove me wrong." Instead of going beyond, simplify. The quantities are the same and the units are what change. Since the quantities remain the same, 1 still equals 1. An apple is not the same as a knife, how many I have can be the same. "By going point by point, my opponent missed my reasoning, and have of his round was filled with misinterpretation of what I was trying to convey, and assume something that in the begin of this round I state to be completely untrue." By going point by point, I was pointing out the flaws of your reasoning in setting up your equations. This was necessary to show the flaw in your reasoning. "By going point by point, my opponent missed that half of my previous round, as I was just trying to demonstrate that, by going by what such of teacher would ... Therefore, the quotient and the divisor cannot represent the same thing." Hopefully, the introduction of units in my argument has answered my opponents objections. The objects become irrelevant. The math remains true and correct as long as the problems are set up properly. The numbers represent quantities of objects, not the objects themselves. When the problem is calculated properly with the units, the quotient and divisor describe the result. "By going point by point, and missing what I did in the beginning, my opponent just use that same argument as I previously show not to work." When the units and problems are set up correctly, they do work. Hopefully I have addressed any misunderstandings from my opponent. Allow me to reiterate as I close this round: The flaws in: my opponents reasoning, setting up of mathematical equations to depict an event, and misunderstanding of units, have left my opponent with an erroneous conclusion. Perhaps I misunderstood his original argument, or perhaps he misrepresented it. That is at this point irrelevant. At the heart of this debate is "A number not always represent the same thing, therefore 1 not always equal 1." Regardless of division, addition, multiplication or addition, using units clarifies the problem as the numbers themselves only represent quantities. 1 will always equal 1. 

Yes, you understood correct, I'm sorry by my mistake. Words that are very close in sound sometimes makes me confused.
I'll try to concentrate on your example, and go over something else that is taught in mathematics, and maybe you could understand my point better. CON wrote; "I have two groups of apples (group A and B). In each group, there is half an apple. I want to figure out how many apples from group A to send to group B. In other words, I want to "divide" my group A members evenly among my group B members. My answer will be:" If you have two groups, and each has half an apple, and you send half an apple to one group, you are left with an empty group (in this case group A). How is this dividing? If you do the same thing with whole numbers, it wouldn't work to gain the result desired. Example: Both groups A and B has 1 apple. I send one apple to group B, group B has now 2 apples. When you divide, you don't start with groups, you have one unit, and you divide that unit. After you divide, you have more than one unit since you split that unit. Let's say I have a bar of chocolate, at this point I have one unit. If I brake this unit in half, now I have 2 half pieces. This can be shown as 1/ 1/2 or 1 / 2 (one divided by two). Both times in the left (represented by the number 1), it will represent the bar of chocolate I had before splitting into 2 pieces. The first equation, the number in the right, represents which way I cut it, which was in half giving me the result of 2 pieces I acquire from that 1 unit. Second equation, the number on the right represents what would happen if I divide this into two groups evenly. Each group would both get half piece. Or you could have the answer to; after dividing the chocolate in two equal parts (groups if you prefer), what size is each part? Anyway, both times, the number in the left is the only number that represent the unit, the number in the right simply tells you what you are doing with that unit. Both numbers never represent the same role. This works great if I have a whole number, but if I have fraction, I cannot do the same, unless the other function on the right is not a fraction. Note* The result 2, even know are chocolates, should be seen as parts because, if you see as chocolates it results in 1=2. I don't know, maybe that is how my opponent arrived on 1 apple from 1/2. Try to follow what I just wrote, but this time use half of a bar of chocolate, and see what happens. If you feel what I say is wrong, please tell me which equation I should have used instead, and use both types of equation to solve both problems, 1 bar of chocolate, and a 1/2 of a bar. If you feel I was right, follow my example using half of bar instead. Now as I promise, I will show what is taught in mathematics, this is not where my thinking originated, but I got to this mathematical concept after this vision of my. Most of us should know that, multiplication is a simpler way to write addition (2+2+2 is the same as 3x2).Like multiplication, division can be written by multiples, but in reverse. So 10/2 could be written, 1022222=5. Two repeats five times, which is the answer. My idea of thinking, lead me to those types of mathematical lessons, I never learn this type of lessons in school.
Thank you to Con for a fun debate! " If you have two groups, and each has half an apple, and you send half an apple to one group, you are left with an empty group (in this case group A). How is this dividing?" It"s not. The division told you how much to send from group a to group b. When you take the half apple from group a, you have subtracted half an apple from half an apple and end up with zero. " If you do the same thing with whole numbers, it wouldn't work to gain the result desired. Example: Both groups A and B has 1 apple. I send one apple to group B, group B has now 2 apples." It does work actually. You have subtracted 1 apple from group a leaving it with no apples. 1 " 1 = 0. And you have added 1 apple to group b which has an apple already. 1 + 1 = 2. " When you divide, you don't start with groups, you have one unit, and you divide that unit. After you divide, you have more than one unit since you split that unit." What you start with depends on how the problem is framed. You didn"t split the unit, you merely ended with a new unit to describe the result. Ex: apple / apple = "apples per apple" In this case, the two units have given you a rate. " Let's say I have a bar of chocolate, at this point I have one unit. If I brake this unit in half, now I have 2 half pieces. This can be shown as 1/ 1/2 or 1 / 2 (one divided by two). Both times in the left (represented by the number 1), it will represent the bar of chocolate I had before splitting into 2 pieces. The first equation, the number in the right, represents which way I cut it, which was in half giving me the result of 2 pieces I acquire from that 1 unit. Second equation, the number on the right represents what would happen if I divide this into two groups evenly. Each group would both get half piece. Or you could have the answer to; after dividing the chocolate in two equal parts (groups if you prefer), what size is each part?" This is an excellent example that demonstrates the equality of the objects based on the unit. One, one half of something is equal to one half of that same something. Two halves are equal to one whole. The amounts are the same, but since you changed the unit, you had to change the quantity to represent the amount. "Anyway, both times, the number in the left is the only number that represent the unit, the number in the right simply tells you what you are doing with that unit. Both numbers never represent the same role." The units have modified the number representing the object. Ex: 2*Pie Radians equal 360 degrees. The numbers are different, as are the units. The amount is the same though, hence the equality. " This works great if I have a whole number, but if I have fraction, I cannot do the same, unless the other function on the right is not a fraction. Note* The result 2, even know are chocolates, should be seen as parts because, if you see as chocolates it results in 1=2. I don't know, maybe that is how my opponent arrived on 1 apple from 1/2." Again, the units describe this. " Try to follow what I just wrote, but this time use half of a bar of chocolate, and see what happens. If you feel what I say is wrong, please tell me which equation I should have used instead, and use both types of equation to solve both problems, 1 bar of chocolate, and a 1/2 of a bar. If you feel I was right, follow my example using half of bar instead." Does 1 = 2? No, however: 1 bar of chocolate = 2 half bars of chocolate. Hopefully, I have fully explained how units are the bridge between math and the real world. 1 = 1. Always. Forever. Thank you for a wonderful debate! 
5 votes have been placed for this debate. Showing 1 through 5 records.
Vote Placed by InquireTruth 4 years ago
Cometflash  GorefordMaximillion  Tied  

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Reasons for voting decision: I bad case of equivocation.
Vote Placed by Azul145 4 years ago
Cometflash  GorefordMaximillion  Tied  

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Reasons for voting decision: This was confusing..... xD
Vote Placed by wrichcirw 4 years ago
Cometflash  GorefordMaximillion  Tied  

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Reasons for voting decision: "Pro's error is confusing numbers with what numbers represent. Con argued the point correctly from the outset."  RoyLatham, genius extraordinaire
Vote Placed by One_Winged_Rook 4 years ago
Cometflash  GorefordMaximillion  Tied  

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Reasons for voting decision: Con wins on the "unit argument" that I don't think Pro ever truly understood
Vote Placed by RoyLatham 4 years ago
Cometflash  GorefordMaximillion  Tied  

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Reasons for voting decision: Pro's error is confusing numbers with what numbers represent. Con argued the point correctly from the outset.
or you can go like this if you want an equation 2=x(1/2) where x is the number of half bars.
just because they refer to different things doesnt mean 2 doesnt always equal 2.
2 half bars equal 1 bar so math 1/2+1/2=1 so 4 halfbars mean 1/2+1/2+1/2+1/2=2
But 2 bars of chocolates doesn't equal 2 half bars of chocolates
two bars of choclate = 4 half bars of choclate so again you have 2=4(1/2) which is the same as 2=2
1 bar of chocolate = 2 half bars of chocolate."
This is pretty much why I said, that an equation on the right that uses addition won't equal the same value on the equation to the left that uses division. I understand that 2 halves of chocolate is the same as 1 whole bar. But 2 bars of chocolates doesn't equal 2 half bars of chocolates. So if you start with two equations one in the right and one in the left, one using adition and on using division, the number you arrive at might not represent the same thing, even if you start with 1 bar of a chocolate in both sides.
You can still try to fix my brain up via PM if you like. :p
The only reason I created such of debate was to gain understanding of what is taught. I actually wanted to end with me understanding and in consequence losing the debate, this why I concentrate more towards understanding what my opponent had to say than my own view.
Believe it or not I was great in math while in shool, but I never really thought about it, I just took the rules that were given to follow and went with it. So even know I was good in math, I guess I didn't had much of understanding.
I used to not understand why some had such of problem with math, maybe the reason is while they were learning, they try to understand, and like me right now, they just could not see it.
"Dear god this is terrible: ... Yes it does. Fail."
LOL HAHAHAHAH
"If we compare 1 apple to 1 orange, it shouldn't be difficult to understand that the "1" in both cases are identical even though what the "1" represents may vary..."
Worded better then I could word it!
It is the Instigators responsibility to make coherent and understandable resolution.