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How Can This Be True?
- Thread starter dimon
- Start date
If A=B then A-B = 0 and you've divided by zero in the third to last step, which is not a valid operation.dimon said:What do you think about this? Do you see anything wrong with this?
A=B
A^2=A*B
A^2-B^2 = A*B-B^2
(A+B)(A-B) = B(A-B)
A+B = B
A = 0 ?
WOW!
Put another way, if X = 0, then 1X = 2X is true, but 1 = 2 does not follow from dividing by X. That's why dividing by zero is not a valid operation: there is no way to define it without getting nonsense.
Hello, dimon!
Here's a variation with a different punchline . . .
(1) We have: . . . . . . . . . . \(\displaystyle A\:=\:B\)
(2) Multiply by \(\displaystyle A:\) . . . . . . .\(\displaystyle A^2\:=\:AB\)
(3) Subtract \(\displaystyle B^2:\;\;\;\;A^2\,-\,B^2\:=\:AB\,-\,B^2\)
(4) Factor: \(\displaystyle \;\,(A\,+\,B)(A\,-\,B) \:= \:B(A\,-\,B)\)
(5) Divide by \(\displaystyle (A-B):\;\;A\,+\,B\: = \:B\)
(6) In (1) we had: \(\displaystyle A\,=\,B\)
\(\displaystyle \;\;\;\) so (5) becomes: \(\displaystyle \;A\,+\,A\:=\:A\)
(7) Simplify: . . . . . . . . . \(\displaystyle 2A\:=\:A\)
(8) Divide by \(\displaystyle A\): . . . . . . . .2 = 1 . . . ta-DAA!
Here's a variation with a different punchline . . .
(1) We have: . . . . . . . . . . \(\displaystyle A\:=\:B\)
(2) Multiply by \(\displaystyle A:\) . . . . . . .\(\displaystyle A^2\:=\:AB\)
(3) Subtract \(\displaystyle B^2:\;\;\;\;A^2\,-\,B^2\:=\:AB\,-\,B^2\)
(4) Factor: \(\displaystyle \;\,(A\,+\,B)(A\,-\,B) \:= \:B(A\,-\,B)\)
(5) Divide by \(\displaystyle (A-B):\;\;A\,+\,B\: = \:B\)
(6) In (1) we had: \(\displaystyle A\,=\,B\)
\(\displaystyle \;\;\;\) so (5) becomes: \(\displaystyle \;A\,+\,A\:=\:A\)
(7) Simplify: . . . . . . . . . \(\displaystyle 2A\:=\:A\)
(8) Divide by \(\displaystyle A\): . . . . . . . .2 = 1 . . . ta-DAA!
dimon, does that mean if I give you a buck, you'll give me two :?: :roll:dimon said:that's even better
3 / 0 = 3dimon said:Sure Denis,
you have got yourself a deal. If, you can ever prove that deviding by zero is a valid operation.
"/ 0" means you're not dividing nuttin'
so you erase "/ 0", and you're left with 3;
if you have 3 beers and divide them up with nobody, then you still have 3 beers...
You owe me 2 bucks :idea: