Using 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.
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Originally posted by XanthosNZso that means that 3 + 3 = 8 as well??? And inversely, 4 + 4 = 6???
(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
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Originally posted by XanthosNZ9 - 21 + (35/4) = 16 - 28 + (35/4) Adding 35/4 to both sides
(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?
(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
(-7/2)*(-7/2) = 49/4Yes 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.
Originally posted by XanthosNZCertainly, I didn't expect you to actually believe your proof. Good job thinking up the completing the square bit.
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.