Originally posted by FabianFnasDepends on which definition of 1, 2, and 3 you're using.
No, not at all pejorative.
From when you enter the math classes in University, you have to wait quite a while before you get the hint why 1+2=3. The reason is that there is so many important things to go through before you go into the very essence of the number systems. You take it for obvious that 1+2=3 and you don't have to care much about it.
So, who can come up with the water strong proof that 1+2=3?
Relatively simple approach, using the axioms of the real numbers:
1 is the multiplicative identity
2 is defined by 2 = 1 + 1
3 is defined by 3 = 1 + 1 + 1
1 + 1 + 1 is well-defined because addition is associative, so (1 + 1) + 1 = 1 + (1 + 1)
1 + 2 = 1 + (1 + 1) = 1 + 1 + 1 = 3
Originally posted by mtthwYou're using Peanos axims for natural numbers, aren't you?
Depends on which definition of 1, 2, and 3 you're using.
Relatively simple approach, using the axioms of the real numbers:
1 is the multiplicative identity
2 is defined by 2 = 1 + 1
3 is defined by 3 = 1 + 1 + 1
1 + 1 + 1 is well-defined because addition is associative, so (1 + 1) + 1 = 1 + (1 + 1)
1 + 2 = 1 + (1 + 1) = 1 + 1 + 1 = 3
Originally posted by FabianFnasAh. Then by the additive property of equality, 1+2=3. Using postulates doesn't simplify the problem much, unless there's one that I'm missing.
No no, 1+2=3 is certainly provable. Just use the axioms. The axioms, on the other hand, is not provable. If they were they are not axioms. And now Gödel comes into my mind.
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Originally posted by FabianFnasFermat already proved this, so I don't have to!!😛.....lol
Wut wait, this 1+2=3 proof, this was meant for Yassy94 ! He wanted math problems. So let him have an another:
Prove that x^n+y^n=x^n for x,y,z reals > 0 and n>2 has not any solutions.
I think I could give you a straight proof, but the input text field is too small...
Just kidding...I like to joke about my lack of mathematical skill..
oh and isn't that supposed to read x^n + y^n = z^n,.....not " x^n + y^n = x^n ?
and just to beat you to the punch....... no, I cant prove it...lol
sorry Andrew Wiles proved it 357 years later than Fermat
Originally posted by joe shmoYou're right, it's a typo. The correct is: x^n+y^n=z^n or course.
Fermat already proved this, so I don't have to!!😛.....lol
Just kidding...I like to joke about my lack of mathematical skill..
oh and isn't that supposed to read x^n + y^n = z^n,.....not " x^n + y^n = x^n ?
and just to beat you to the punch....... no, I cant prove it...lol
sorry Andrew Wiles proved it 357 years later than Fermat
But leave this little problem to Yassy94. Don't give away the answer too quickly.
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Is this supposed to be some sort of difficult problem? With a small knowledge of properties and the "plug it in method" it is obvious that those inequalities are correct.
I suppose proving it is something else. I am in summer school now and I believe we are covering proofs next week in trig. To tell the truth I never heard of a "proof" in math before hearing it in class the other day.
