# prove that: 2=1

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### 3 Answers

2=1, cannot be proven.

Both "proofs" above, divides by a 0. A number can not be divided by 0 because in essence it's like trying to take a group and divide into a group of nothing. A group already exist, to make it vanish will be subtraction not division.

a-a, from "wakeuprj" means a number minus itself so that is 0.

a-b, from "samantha96" is 0 because the assumption was made that a=b meaning a and b are the same number. Using additive inverse, subtract b from both sides a-b=0.

2=1 is obviously wrong and inlogical, mathematicians have no problem to admit something is not true.

**a = b**

multiply both sides by a

**a^2 = a*b**

subtract b^2 from both sides

**a^2-b^2 = a*b-b^2**

apply the distributive law to both sides

**(a+b)(a-b) = b(a-b) **

divide both sides by (a-b)

**(a+b) = b**

substitute all a's for b's (remember, if a = b you can do this)/

**a+a = a**

regroup the two a's in the left side, and rename it 2a

**2a = a**

divide both sides by a

**2 = 1**