Is there any flaw in this proof that 1/0 is not a real number?

Question

skullpatrol · Answer

Given a real number "a" we may find a number 1/a such that a • (1/a) = 1; except if given the number 0, we know we can not find a number 1/0 such that 0 • (1/0) = 1 because 0 • (any real number) = 0. Therefore, 1/0 can not be any real number because if it was a real number 1 = 0.

weasel123 · Answer

this all u?

weasel123 · Answer

wow. i need to rethink da world

jhonyy9 · Answer

this fraction 1/0 is undefined - denominator not can being zero never

kainui · Answer

If you say "All real numbers have inverses" as your definition, then this definitely means 1/0 is not a real number by definition.

usukidoll · Answer

isn't there an axiom somewhere which gives out three cases?
1=0
1<0
or 0<1 ???
and then we have to prove that only one of them is exactly true?

directrix · Answer

^^^
Trichotomy Axion  @UsukiDoll 

At first glance, your argument seems like circular logic to me. @skullpatrol

skullpatrol · Answer

What do you @Directrix think about the logic used here:

Why can you never divide by zero?


Dividing by zero would mean multiplying by the reciprocal of 0.

But 0 has no reciprocal (because 0 times any number is 0, not 1.)

Therefore, division by 0 has no meaning in the set of real numbers.