prove that: 2=1
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