Math problem

Originally posted by FabianFnas
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?

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 mtthw
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

You're using Peanos axims for natural numbers, aren't you?

Originally posted by FabianFnas
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.

Ah. 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.

Originally posted by FabianFnas
You're using Peanos axims for natural numbers, aren't you?

Probably 🙂

I suspect proofs using the set theory definitions of cardinal numbers might be more interesting, but I don't remember much set theory!

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...

Originally posted by FabianFnas
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...

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

Originally posted by joe shmo
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

You're right, it's a typo. The correct is: x^n+y^n=z^n or course.

But leave this little problem to Yassy94. Don't give away the answer too quickly.

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.

Okay. It's provable because if you there are 2 books on a shelf and you ADD one to the shelf, you have 3.

wat about that 3n + 1 problem?
still unsolved i think?

With the fermat last theorm look-a-like problem, there is a really short proof involving modular arithmetic. One-line proof, in fact, if you start far enough to the left of an A4 sheet of paper.

Originally posted by banx99
wat about that 3n + 1 problem?
still unsolved i think?

Is that the problem Which leads to 1 when performing the operations, If it is, then I ve read that they are offering a reward for it proof!

Originally posted by Yassy94
Okay. It's provable because if you there are 2 books on a shelf and you ADD one to the shelf, you have 3.

Great. You have proved a SPECIAL CASE.







. A bookcase 😀

um.. Thanks!

Originally posted by Yassy94
um.. Thanks!

no problem