1x1=2

essentialsaltes said:

You can't prove anything without a logical system, and a logical system needs axioms.

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leftrightleftrightleft said:

No they aren't. They logically follow from axioms.

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FrumiousBandersnatch said:

It was Russell and Whitehead who sorted out the details in Principia Mathematica, using symbolic logic to explicate the logical foundations of mathematics, building up to 1+1 =2, and so-on. It only took a few hundred pages...

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The Cadet said:

They were then proven completely wrong.

https://en.wikipedia.org/wiki/Gödel's_incompleteness_theorems

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Also this thread physically pains me.

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crjmurray said:

After high school, he attended Pratt Institute in Brooklyn, studying chemical engineering, until he got into an argument with a professor about what one times one equals. "How can it equal one?" he said. "If one times one equals one that means that two is of no value because one times itself has no effect. One times one equals two because the square root of four is two, so what's the square root of two? Should be one, but we're told it's two, and that cannot be."

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Chriliman said:

I wouldn't be surprised if the very foundation of mathematics is based on falsehood.

What does it mean to 'times' something? Take an amount and duplicate it by another amount. So if you take 1 and duplicate it 1 time, you have to 2. If you take 2 and duplicate it 2 times, you have 4. Makes sense to me.

Edit: now that I look at that again, if you have 2 and duplicate it 2 times you have 6. Something doesn't seem right there...

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Freodin said:

But that is not the problem with this skit.

So you think that the "redundancy" is what makes it wrong?

Let's do it again, then!

a = a (Axiom or not, it is correct)
a^2 = a^2 (Multiplying both sides of an equation with the same factor doesn't change the equality, so correct)
a^2 - a^2 = 0 (Subtracting the same value on both sides... still correct)
(a-a)(a+a) = 0 (valid transformation according the the binomic formulas... correct)
(a-a)(a+a)/(a-a) = 0/(a-a) (Dividing both sides with the same value... correct)
1(a+a) = 0 (reducing a fraction by eliminating equal factors in counter and denominator on the left side, using the fact that 0 multiplied by any fraction stays 0 on the right side of the equation... both correct.)
(a+a) = 0 (simplifying by just dropping the factor of one... correct)
1 + 1 = 0 (inserting a value... correct)
2 = 0 (computing the values... correct)
1 = 0 (not sure what was done here... division by 2? Still, correctly done.)
1 + 1 = 1 (using the last equation within a new calculation... if we were correct up to now, we can do this. So... correct.)

So, no redundancy anymore. Just one variable used.

Where is the problem?

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