A Fallacy On Number
Is one equal to zero?
Lets assume:
a=1
b=1
we can say:
1. a = b given
2. a x a = b x a multiply both sides with a
3. a^2 = ab simplify result
4. a^2 - b^2 = ab - b^2 subtract b^2 on both sides
5. (a+b)(a-b) = b(a-b) factor
6. a + b = b divide both sides with (a-b)
7. a = 0 subtract b on both sides
8. 1 = 0 substitute
Lets assume:
a=1
b=1
we can say:
1. a = b given
2. a x a = b x a multiply both sides with a
3. a^2 = ab simplify result
4. a^2 - b^2 = ab - b^2 subtract b^2 on both sides
5. (a+b)(a-b) = b(a-b) factor
6. a + b = b divide both sides with (a-b)
7. a = 0 subtract b on both sides
8. 1 = 0 substitute
posted by Ozting at 5:27 PM
3 Comments:
Cool! I tried it with the numerical values of a and b, and it still made sense! Hehe! Nice...
Really Claire? I would like to point out that in step 5, 1/(a-b) was multiplied to it to come with equality in step 6. It looks like a valid mathematical operation (i.e. multiplication property of equality) but if you notice, 1/(1-b) is actually 1/0 which is undefined. In other words, you try to divide step 5 by 0 to come up with step 6 and your high school math tells you that division by zero is never allowed. Thus, making steps 6-8 invalid.
That's why it called a fallacy.
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