Are Mathematicians Silly?
Debate Rounds (3)
Definition of silly: lacking common sense or judgement
Here are just some reasons why I believe they are silly:
1. Mathematicians believe that 1 2 3 4 ...(to infinity) = -1/12
2. Mathematicians believe the repeating decimal 0.999... = exactly 1
3. Mathematicians believe there are 360 degrees in a circle
4. Mathematicians believe there just as many even numbers as there are natural numbers.
I do not believe mathematicians are silly. I believe that their conclusions are based on common sense or judgement. I will start by stating why mathematicians believe the things that you have written in your round 1 argument.
1) Mathematicians believe that 1+2+3+4 ... (to infinity) = -1/12 PLUS infinity because of a logical explanation. The logical explanation is that the = in the equation does not mean "is equal to" in this situation, rather, it means "is associated with" (1). Yes, this is tricky, but that does not mean mathematicians are silly, otherwise, all tricky people would be known as silly (which is not the case). After that, it starts to make sense, as you simply need to do some algebra to prove it. You can look at a proof at https://plus.maths.org....
2) For all intents and purposes, .9 repeating equals exactly 1. A simple algebra proof does the trick here:
Let's say x= .9 repeating. Then 10x=9.9 repeating. Now subtract the equation x=.9 repeating from 10x=9.9 repeating, and you get 9x=9. Then you simplify, and get x=1. x=.9 repeating AND x=1, so .9 repeating equals exactly 1. Also, 1/3=.3 repeating. 3/3=.9 repeating, and 3/3=1, so .9 repeating equals exactly 1. If you don't believe, you can find it here: http://polymathematics.typepad.com...
3) There are 360 degrees in a circle. It is taken for granted by this source that we all learn this during our childhood education: http://math.rice.edu.... This has been the case since ancient times, as a 360 degree circle made the most sense to these people (this is because their calendars were 360 days long) (2). If you can find a circle that is not 360 degrees, then kudos to you. This is because you won't be able to.
4) There are as many even numbers as there are natural numbers. This is because both are a list of infinite numbers. Infinity = Infinity. This should be obvious using common sense.
Now, you said those are just some of the reasons you believe mathematicians are silly. Let's look at the definition of mathematician:
Mathematician: a person who is an expert in mathematics (3)
Now, the only difference between mathematicians and everyone else is that they are experts in mathematics. So you are saying that mathematics is silly, or else by common sense you would be saying that everyone in the world is silly. Now, you could argue that everyone in the world is indeed a bit silly. However, there are plenty of people whose common sense and judgement outweigh their silliness, negating that argument. Now let's focus on whether or not mathematics is silly.
Mathematics start with basic mathematical concepts and the concepts gradually become more complex, leading to formulas, theories, etc. A natural question that arises is, 'How did those original basic mathematical concepts come about?' The answer is common sense. Let's take geometry as an example. We start by drawing a couple segments. There is no way to prove the segment addition postulate (where a point B on segment AC makes it so that AB + BC = AC) (4). It just makes common sense. You can build on this postulate with the midpoint theorem, and then combine this theorem with other theorems derived from other postulates, and eventually you can get theorems and formulas such as the Pythagorean Theorem, Distance Formula, etc. Now, the reasons you listed above may not seem like common sense, but they are all still rooted in common sense.
As you can see, mathematics are not silly, as they are rooted in common sense. Therefore, you cannot call mathematicians silly, unless you are calling all humans silly. Granted, there are probably some mathematicians that are silly as people, but this is the same with all other groups of people.
I have shown that mathematicians are not silly, it is now up to Pro to prove that mathematicians are indeed silly.
Before I begin, I want everyone to know that I don't believe everyone is silly, it's just that when we go further in the field of maths things start to get silly and some of these things get taught.
1. I did watch the numberphile video about this, and immediately knew those mathematicians were wrong (or silly). I've tried to understand this, and even after reading your source I just can't get where -1/12 comes from. Perhaps it's best to ignore this point.
2. I didn't realize there were so many ways to show 0.999.. equals 1, see below
The simplest is: 0.1111... = 1/9
multiply both sides by 9
0.9999... = 1
Your method is: A = 0.999...
Then 10A = 9.999...
10A - A = 9.000...
A = 1
Let's look at the first one, my instinct is not to type 0.999... when I multiply 0.111... by 9. I'd simply put 1.
It just seems like a clever trick to show 0.999 and 1 are the same thing, when really when we say 0.111... is 1/9 it is because this is the best way to show what one ninth is in a decimal format.
Mathematicians say that 0.999... and 1 are the same because there is no number between them, however I believe there is. This number is 0.00000.....1 which is basically an infinitely small number.
Take a look at the below to see where my idea is from:
0.9 + 0.1 = 1
0.999 + 0.001 = 1
0.999999 + 0.000001 = 1
if I have 1 million 9's after 0, then I need an equal number of 1 million minus 1 zeros before 1. I thus need to make an addition to make a whole number.
Mathematicians say that 0.999999... = 1 ,meaning that 0.00...1 is equal to EXACTLY ZERO
let's make k = 0.000...1
S = 0.999.. i.e. 1 - k
10S = 10 - 10k
(10 - 10k) - (1 - k) = 9 - 9k
S = 1 - k
You may tell me that it should look like the below:
S = 1 - k
10S = 10 - k
(10 - k) - (1 - k) = 9
9S = 9
S = 1
Though 10k are both indefinitely small, they are not the same, and therefore should not be treated the same! Doing so is BAD MATHS in my opinion.
Imagine if I lost half of my money every second and someone else lost a quarter of their money each time, it is natural to say we will both end up with "nothing" but the pattern actually continues for eternity. Applying this maths someone can have an infinite amount less than me if we could live forever. But it is possible to make it so that a person always has 10 times less than me.
Let's move on now..
0.999... = 0.9 + 0.09 + 0.009 + 0.0009 etc
1 = 1 + 0...
So, basically 0.999.. is ALWAYS less than 1, and by an infinite amount i.e. 0.00...1
If you want further proof that 0.000.... 1 is not zero, consider a triangle and a circle, they appear different because they have different internal angles.
3. It should be obvious that a circle doesn't have 360 degrees, because a square has 360 degrees and is a different shape. A line was chosen to have 180 degrees (something had to be chosen), and from this we can calculate the number of degrees in every polygon.
I'll do some simple calculations I learnt from school and see if you can see a pattern emerge
let's take a square which as you know has 4 sides,
360/4 = 90 degrees
There are 180 degrees in a triangle, so the other angles add up to 180 - 90 = 90
There are 4 sides, so a square has a total of (4 x 90) degrees = 360 degrees
If we have a 16 sides shape now
360/16 = 22.5 degrees
There are 180 degrees in a triangle, so the other angles add up to 180 - 22.5 = 157.5
It will therefore have total of (16 x 157.5) = 2520 degrees
If we have a million sided shape now
360/1 million = 0.00036
There are 180 degrees in a triangle, so the other angles add up to 180 - 0.00036 = 179.99964
It will therefore have (1 million x 179.99964) = 179999640 degrees
As you can see the more sides there are in a polygon the closer the angle "OF ONE SIDE" becomes to 180. f you don't believe me you can try my method with polygons of more sides. The internal angle can never be 180 though because only a straight line has 180 degrees. So a circle has 179.999... degrees
4. There are an equal number of odd and even numbers, so why do Mathematicians say there are just as many even numbers as there are natural numbers, it seems silly to me.
If you line them together
You might think there is just as many, but arranging them in a sequence like above ignores what natural numbers are, see below
1, (2), 3, (4), 5, (6), 7, (8)
Even numbers are part of a sequence, there will always be two times more natural numbers than even numbers. To think otherwise is silly.
Thanks for reading, hope I didn't waffle too much.
1) In the comments, I agreed to disregard this. You can still look further into this if you want.
2) .1 repeating is indeed "the best way to show what one ninth is in a decimal format." This is because it is 1/9 really does equal .1 repeating. Divide 1 by 9 using long division, which I'm sure you can do. Then there can be no doubt that .1 repeating equals 1/9. And .1 repeating times 9 is .9 repeating, and 1/9 times 9 is 9/9, or 1. There is now no doubt .9 repeating is 1. If you still want more information on this topic, look at this source: http://www.purplemath.com...
3) Pro misunderstands something essential. What you have found in your round 2 argument is an internal angle sum of a polygon The internal angle of a polygon is the angle on the inside of a polygon formed by a pair of adjacent sides (1). The sum of the internal angles in a square are 360 degrees. However, the 360 degrees in a circle are not talking about the internal angles as in the definition above. Rather, they refer to the combined degree measurement of the non-overlapping central angles in a circle. The definition of a central angle is an angle subtended at the center of a circle by two given points on the circle (2). These angles are definitely completely different things. Now, a circle most definitely has 360 degrees if we use non-overlapping central angles. My opponent has misunderstood what angles mathematicians are referring to when they say there are 360 degrees in a circle.
4) Yes, if you end the list of even and natural numbers at a certain point, there will be more natural numbers than even numbers (actually, perhaps not necessarily so, which I'll explain later). However, the list of natural numbers goes on forever, which I'm sure you agree with. The list of even numbers goes on forever, which I'm also sure you agree with. Both sets of numbers have an infinite amount of numbers in them, therefore, there are an equal amount of natural numbers as even numbers, as infinity = infinity, which makes common sense. Also, the definition of an even number is a number that can be divided by 2 (3). Therefore, negative numbers can be even too. So even if you do decide to end the sets of numbers at a finite point, there will still be the same amount of even and natural numbers.
I will end this round by reiterating the point that my opponent has not proved that mathematicians are silly. Rather, he has played into my hands by using math, which he is trying to prove is silly. My opponent is trying to prove that math is silly because, as I said in round 1, the only difference between mathematicians and everyone else is that they are experts in math. Now, my opponent stated that he doesn't believe everyone is silly in Round 2, so as a result he must prove math is silly to prove that mathematicians are silly. Now, by using math, which he is trying to prove is silly, and using it thinking that it is sensible, he is in fact destroying his own argument. It is now up to Pro to fix his argument, and to somehow prove that math, and by extension mathematicians, are silly, as I have proven that math is based on common sense in round 1.
"there is a thing in math called an axiom. It"s a statement assumed to be true without proof. One axiom underlying the real number system basically says: Non-zero infinitesimals do not exist. Which means 0.000"1 does not exist"  Why? because mathematicians say so.
"A person who thinks 0.999" doesn"t equal 1 obviously believes infinitesimals exist. They don"t accept that axiom." 
Here is a source you will like [see source 2]. There are lots of different arguments to support the idea that 0.999... equals 1, however I don't think I need to prove everyone of these wrong to prove mathematicians are silly, and I certainly don't need to use maths. If I look at the sum 1.0... minus 0.9... I will get 0.000...1 which is basically a string of infinite zeros followed by a 1, you may ask how can we put that 1 at the end if there are an infinite number of zeros before it?
I wouldn't be able to ever write that 1 at the end, but this doesn't mean it is not there. If we look at a straight line, it has 180 degrees, if you curve that line it must curve to either the left OR the right. How much does it curve in either direction? An infinitely small amount believe it or not. Saying a circle has 360 degrees hides a circle's true properties, which is silly, especially when there is absolutely no good reason for doing so.
You say I used maths for reasons 2, 3 and 4. But I have not used anything we don't all learn at school, and we aren't all mathematicians! Though I used maths to show the exact angle of a circle, I could just use common sense and say that if I add more sides to a polygon the angle inside will get flatter i.e. closer to 180, and because I could add any number sided polygon inside a circle, it's pretty obvious without doing the calculations that the angle of one side will never reach 180. Maths itself is not silly, however mathematicians can be e.g. by believing that there are 360 degrees in a circle. It's not silly for the average person to believe this if they don't try to understand maths. Someone would have to believe in a lot of silly ideas to be classed as silly, not just part silly, and there is more e.g. mathematicians have all sorts of silly definitions like "composite numbers" which is an integer greater than one that is not a prime number. Is that necessary? A composite number is just a Square and a Rectangle number. What will they call a Triangular number and a Square number, or Pentagonal number and a Rectangle number, it's silly. A triangle number counts the objects that can form an equilateral triangle, so what do you call a number which doesn't count objects that form an equilateral triangle? I'm sorry, but it seems silly to me.
If I have misunderstood what angles mathematicians refer to then it is because mathematicians are silly. Mathematicians do not show angles in more than 1 decimal place, so that means they use a polygon with 6,476,40 degrees to make angle measurements. Inches can be converted to centimetres, miles can be converted into kilometres etc, so why don't mathematicians use a different measurement if they don't like working with large numbers? Because they are silly.
The list of natural numbers and even numbers both go to infinity, but if we say there is an equal number of even and natural numbers this implies that if we stop at one point along the sequence of natural numbers then we will have an equal number of natural and even numbers. Every difference should be accounted for, if you don't then it's possible to trick people into believing silly things like 0.999... equals 1.
2) Your own "source," the non-reliable blog, states that .9 repeating does equal 1 depending on the type of math being used. Mathematicians that go by this math and believe .9 repeating = 1 aren't silly at all then, according to your own "source," and this is assuming that everything in your "source" is correct. Also, as the majority of mathematics does NOT deal with non-zero infinitesimals, it was assumed that you were speaking of the (larger) part of mathematics that doesn't deal with non-zero infinitesimals, as it only makes sense that was what you were talking about. Pro cannot just come in and state in the last round that we are using non-zero infinitesimals. If we aren't, then my proofs are all 100% valid. Therefore, it is not at all silly to believe that .9 repeating equals 1. Your own "source" even states so: "If you feel it (.9 repeating) does equal one, you"re right too." Also, your second source only supports my argument. I believe you only included it just to have a reliable source, however, if one reads that source, they find many arguments supporting the statement .9 repeating equals 1. So even the "sources" supporting Pro's argument actually support my argument, that mathematicians are not silly. As you can see, it is not at all silly to believe that .9 repeating equals 1.
3) Pro states, "Maths itself is not silly, however mathematicians can be e.g. by believing that there are 360 degrees in a circle." In that paragraph, Pro is (once again) trying to state that there are not 360 degrees in a circle because of the fact that regular polygons start to have greater angle measurements as they have more sides. Once again, Pro has shown in this paragraph that Pro doesn't understand what angles we are talking about. I clarified in Round 2 that the 360 degrees in a circle refer to the measure of the sum of the non-overlapping central angles, NOT the sum of the internal angles (by the way, there are no internal angles in a circle). However, the angles in the polygons that Pro refers to in that paragraph I mentioned earlier are internal angles. At this source (https://www.mathsisfun.com...) the angle that measures 30 degrees is the interior angle. For an example of a central angle, look at http://www.mathopenref.com.... As you can see, two completely different things! The angle on the image (for the second source mentioned in this paragraph) is a central angle. If you create a straight line of 180 degrees (by dragging the orange points on that site), you can see that there are obviously two of those 180 degree angles making up the sum of the non-overlapping central angles, and obviously 180 times 2 equals 360. Therefore there are 360 degrees in a circle! Obviously Pro is incorrect here. Mathematicians believe that there are 360 degrees in a circle because they refer to the sum of the non-overlapping central angles in a circle. As this is true, this is by no stretch of imagination silly. Pro then later mentions that if Pro has "misunderstood what angles mathematicians refer to then it is because mathematicians are silly." How does this make any sense at all? Pro is basically saying that it is the fault of the mathematicians that he was unable to look carefully enough into the subject to see what angles mathematicians were referring to. By all means this is incorrect, as one can easily see. Later in Pro's second to last paragraph, he goes into meaningless jumble about units. No matter how I look at it, I cannot fathom how the units have anything to do with the degrees in a circle. Pro makes no sense here.
4) Pro doesn't even try to disprove that there are the same amount of even numbers as natural numbers. This is because there are. Let's think about this:
Even numbers include negative numbers that can be divided by 2.
Natural numbers don't include negative numbers.
Let's take the numbers 1 to 4. There are 4 natural numbers (1, 2, 3, 4) and 2 even numbers (2). But let's add -2 and -4 to this set, and there are an equal amount of even and natural numbers. Do the same thing with (5, 6, 7, 8) by adding -6 and -8, (9,10,11,12) by adding -10 and -12, etc, and get a equal amount of even and natural numbers.
Now for other arguments:
I have now proven that all of Pro's examples of "silly mathematics" are actually valid and based on solid math, and as I have proven that math is based on common sense in Round 1, these examples are in turn based on common sense, making these concepts, as well as mathematicians that believe these concepts, the opposite of silly. Pro states that another reason Pro believes mathematicians are silly is because they come up with silly definitions. This means that Pro believes these definitions are lacking in common sense. This is completely subjective and opinionated. Pro cannot decide that since certain definitions don't make sense to him, they are silly. Pro must have deeper reasoning, which he doesn't have. Although Pro may think that the definitions of mathematicians don't make sense, what if I do? Why does his opinion count for more than mine? It doesn't. Pro's argument there is completely invalid.
I will just state that math has to be proven silly for mathematicians to be full-silly. Otherwise, as mathematicians are the ones that came up with all of this math, if any of the math is correct, even if a few concepts are silly, you cannot say that mathematicians are silly.
In conclusion, I have proven that Pro's examples of "silly mathematics" are really based on common sense. Pro's argument was that since mathematicians believe those silly things, they are silly, however, as I have proved those silly things are actually not silly, that argument has been proven wrong. Over the course of the debate, I also proved that math was not silly, and as math is the only thing that separates mathematicians from the rest of us, I proved here that mathematicians are not silly. I have left Pro with nothing of his argument, so as a result, I have successfully proven that mathematicians are not silly, rather, I proved that their conclusions were based on common sense. I have had the better sources in this debate, as well. Thank you, mostlogical, for providing such a good debate.
1 votes has been placed for this debate.
Vote Placed by salam.morcos 1 year ago
|Who won the debate:||-|
Reasons for voting decision: Pro claimed that mathematicians are silly, but didn't define silliness. Pro's arguments don't show that mathematicians are silly. It only shows that he finds them strange. Con did an excellent job of why all the different "strange" things are logical and reasonable. People might think that it's strange that we live on a round planet, but not falling from it. Strange doesn't mean silly. I vote con.
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