- 22 Oct '04 09:23Using axioms of mathematics;

3+4 = 4+3 this is the communitative property of addition.

4+3 = 4+(2+1) this is the definition of 3

4+(2+1) = 4+(1+2)

4+(1+2) = (4+1) +2 this is the associative property of addition

(4+1) +2 = 5+2 this is the definition of 5

5+2 = 5+(1+1) this is the definition of 2

5+(1+1) = (5+1) +1

(5+1) +1 = 6+1 this is the definition of 6

6+1 = 7 this is the definition of 7

Proof above shows 3+4=7, nothing more, nothing less.

Now by assuming 0=1 or some other equivalent statement, it's easy to show 7=8, making 3+4=7=8. Alas, 3+4 would equal anything then. - 23 Oct '04 02:33(3^2) - 21 = (4^2) - 28

9 - 21 + (35/4) = 16 - 28 + (35/4) Adding 35/4 to both sides

(3 - (7/2))*(3- (7/2)) = (4 - (7/2))*(4 - (7/2)) Factorising

(3 - (7/2)) = (4 - (7/2) Taking the square root of both sides

Therefore 3 = 4

Substituting into the equation 4 + 4 = 8

we get 4 + 3 = 8

How's that? - 23 Oct '04 14:30 / 1 edit

so that means that 3 + 3 = 8 as well??? And inversely, 4 + 4 = 6???*Originally posted by XanthosNZ***(3^2) - 21 = (4^2) - 28**

9 - 21 + (35/4) = 16 - 28 + (35/4) Adding 35/4 to both sides

(3 - (7/2))*(3- (7/2)) = (4 - (7/2))*(4 - (7/2)) Factorising

(3 - (7/2)) = (4 - (7/2) Taking the square root of both sides

Therefore 3 = 4

Substit ...[text shortened]... ting into the equation 4 + 4 = 8

we get 4 + 3 = 8

How's that?

D - 23 Oct '04 16:29 / 1 edit
*Originally posted by XanthosNZ***(3^2) - 21 = (4^2) - 28**

9 - 21 + (35/4) = 16 - 28 + (35/4) Adding 35/4 to both sides

(3 - (7/2))*(3- (7/2)) = (4 - (7/2))*(4 - (7/2)) Factorising

(3 - (7/2)) = (4 - (7/2) Taking the square root of both sides

Therefore 3 = 4

Substit ...[text shortened]... ting into the equation 4 + 4 = 8

we get 4 + 3 = 8

How's that?**9 - 21 + (35/4) = 16 - 28 + (35/4) Adding 35/4 to both sides**

(3 - (7/2))*(3- (7/2)) = (4 - (7/2))*(4 - (7/2)) Factorising

Uhm . . . you also have an arithmetic error.

(-7/2)*(-7/2) = 49/4

ok let's say you changed 35/4 to 49/4

you basically have (-1/2)*(-1/2) = (1/2)*(1/2) True.

but the next line is equivalent to -1/2 = 1/2 False.

Problem? sqrt(1/4) = 1/2 or -1/2

From this however we cannot say that 1/2 = -1/2

- 23 Oct '04 21:47
(-7/2)*(-7/2) = 49/4

Yes you're right. It seems I can't multiply. You are also right in finding the flaw in the logic of my argument. Of course it's there. You don't actually think I can prove 3=4 without one do you? There is the more common 'proof' of 1=2 that uses dividing by zero.

ok let's say you changed 35/4 to 49/4

you basically have (-1/2)*(-1/2) = (1/2)*(1/2) True.

but the next line is equivalent to -1/2 = 1/2 False.

Problem? sqrt(1/4) = 1/2 or -1/2

From this however we cannot say that 1/2 = -1/2

Nice eyes spotting the mistake though. First time round it took me a while. - 23 Oct '04 22:37

Certainly, I didn't expect you to actually believe your proof. Good job thinking up the completing the square bit.*Originally posted by XanthosNZ***Yes you're right. It seems I can't multiply. You are also right in finding the flaw in the logic of my argument. Of course it's there. You don't actually think I can prove 3=4 without one do you? There is the more common 'proof' of 1=2 that uses dividing by zero.**

Nice eyes spotting the mistake though. First time round it took me a while.