The Instigator
emil1
Pro (for)
Losing
0 Points
The Contender
Mikal
Con (against)
Winning
8 Points

Why is 1 + 1 =2

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Post Voting Period
The voting period for this debate has ended.
after 2 votes the winner is...
Mikal
Voting Style: Open Point System: 7 Point
Started: 9/6/2013 Category: Education
Updated: 4 years ago Status: Post Voting Period
Viewed: 1,140 times Debate No: 37430
Debate Rounds (1)
Comments (11)
Votes (2)

 

emil1

Pro

1 + 1 = 2 because if you have one item and add another item to it you have 2 items. Therefore, using this example, 1 + 1 = 2
Mikal

Con

I will argue this from two perspectives. I agree with the outcome but not with resouition he stated. I will show that 1+1=2 but not with the logic he presents. I will also show how 2 can equal 1 or 2=1


Contention 1

Postulates

I am arguing this based off his resolution. I do agree 1+1= 2 but not because of the stance he gave. He states this

"1 + 1 = 2 because if you have one item and add another item to it you have 2 items. Therefore, using this example, 1 + 1 = 2"


If you have an item and add another item to the first, it does not always make 2 items. The 2 items could merge and make one item.

Example 1+1=11

By taking 1 and adding it to another 1, you are showing that side by side the could make 11 or even become one item and make the number 11.



We know 1+1 = 2 by a rule guideline that is refereed to as the Peano Postulates

It pretty much states this word for word


"1. 0 is a number.
2. The successor of any number is also a number.
3. No two distinct numbers have the same successor.
4. 0 is not the successor of any number.
5. If any property is possessed by 0 and also by the successor of any number having that property, then all numbers
have that property."

This is basically defining what the + is, and stating that every successor of a number can not have the same successor. Pros resolution is not refined, and I can arrive at any conclusion with the guideline he presented.



Contention 2

Classic Fallacies

I could Claim that 2 = 1 or 1 equals itself.


This is arrived at using basic algebra

"a = b
a2 = ab
a2 - b2 = ab-b2
(a-b)(a+b) = b(a-b)
a+b = b
b+b = b
2b = b
2 = 1"


or that 1+1=1

"a = b
a2 = b2
a2 - b2 = 0
(a-b)(a+b) = 0
(a-b)(a+b)/(a-b) = 0/(a-b)
1(a+b) = 0
(a+b) = 0
1 + 1 = 0
2 = 0
1 = 0
1 + 1 = 1"


Contention 3

Principa Mathematica


This is a book by Russell White head which attempts to explain this very question. Again it shows that adding one thing to another is not the cause of 1+1 =2



This adds to the first contention but these are some of the points the volumes try to encompass

It goes on to show what inductive relations are and the essence of assigning values to the numbers in which you are using

View the youtube video above



In Closing

His resolution is false.

1+1 does equal 2 but not by the logic presented.

http://quod.lib.umich.edu...
http://plato.stanford.edu...
http://mathworld.wolfram.com...
http://myhome.spu.edu...










Debate Round No. 1
11 comments have been posted on this debate. Showing 1 through 10 records.
Posted by Shadowguynick 4 years ago
Shadowguynick
Although Mikal won, your simple algebra was wrong. You have to do the same thing to both sides of the equation, so you cannot go from a=b to a2=ab since you are multiplying by two on one side and squaring on the other side. I am hoping you already knew this, but just in case not.
Posted by Mikal 4 years ago
Mikal
for the tenth time read what the title is.

That is why I called it a logical fallacy
Posted by eholzer 4 years ago
eholzer
I hate to break it to you Mikal but your "simple algebra" is wrong.
in this problem:
1 ."a = b
2. a2 = ab
3. a2 - b2 = ab-b2
4. (a-b)(a+b) = b(a-b)
5. a+b = b
6. b+b = b
7. 2b = b
8. 2 = 1"

if a=b then a-b is zero
if a-b in zero than you cannot divide by a-b in step 4
if you divide by zero then the equation is undefined which would make 1 not equal 2
Posted by Mikal 4 years ago
Mikal
I never claimed it was true. Does no one read the title of the section. I have said that three times.
Posted by emil1 4 years ago
emil1
Spaceman_Guy... can you vote
Posted by Spaceman_Guy 4 years ago
Spaceman_Guy
Contention two is false. You do not understand factoring. Its still interesting though.
Posted by emil1 4 years ago
emil1
Simplicity does not kill. My argument made sense. It depends on the voter to like simplicity or complex. Bet you that most of the voter (2 or 3) doesn't even have gotten the your idea because it was way too complex.
Posted by Mikal 4 years ago
Mikal
Faulty is the same thing as fallacy by the way, which is why I labeled it logical fallacies.

Ergo you have to define the values or 1 could take on any identity. Which is contention 3. Also there is a whole book about this written, I had to read some of it back in college. The link is there if you want to refine your statement.
Posted by Mikal 4 years ago
Mikal
That is the point of the debate, if he states a resolution he has to support it. His claim if false. Simplicity kills
Posted by ProgressiveSlayer 4 years ago
ProgressiveSlayer
I WOULD VOTE, BUT MY ACCOUNT WON'T LET ME VERIFY MY IDENTITY:

Con's logic is fallible. In argument 1 he states that adding one object to another can end up with things merging, this though true, is not topical. He essentially makes a straw man argument by taking the example that Pro used to prove his theory of objects. In reality the topic is talking about the idea of 1, Pro used the object theory correctly whereas Con did not. Con's 2nd argument was completely ludicrous for example
a = b
a2 = ab
That is wrong, in order to have a proper flow of equations you must do the same thing to each side, you may say "but a = b so it is 2a" but this is wrong because it would actually be a^2 = ab.....
in the second equation he states that
a2 - b2 = 0
(a-b)(a+b) = 0
but this is also faulty. it would actually end up being 2(a-b)=0..
Con's only argument left is a complex argument that he also expended a sentence on. You should always explain your sources, they are not there to add to your words, only to back them up.....

Pro wins because of his simplicity, where Con lost because he neglected to back up any of his more complex arguments. He failed through logical fallacies, errors in math, or just plain not expounding on information.

I WOULD VOTE, BUT MY ACCOUNT WON'T LET ME VERIFY MY IDENTITY:
2 votes have been placed for this debate. Showing 1 through 2 records.
Vote Placed by Sargon 4 years ago
Sargon
emil1MikalTied
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Total points awarded:03 
Reasons for voting decision: This debate is not whether 1 +1 = 2. This debate is about the reasoning that supports the conclusion. This means that both debaters can agree that 1+ 1 =2, while simultaneously disputing the reasoning why. Con clearly and concisely showed, using the history of mathematics, why the resolution is true. Pro's statement begged the question and didn't answer anything. Due to the effectiveness of Con's explanation, the shortness and tautological argument from Pro, and the fact that Con's statements could not rebutted, I give Con arguments.
Vote Placed by Bullish 4 years ago
Bullish
emil1MikalTied
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Total points awarded:05 
Reasons for voting decision: CON had 3 arguments while PRO basically just repeated his resolution. CON also had sources.