If a/b = 0 then a=0

a/b=0 implies a=0 for all values of b except infinity

a/b=0
a/0=b and 1/0 isinfinity
so b=infinite if a is not a 0 too

if b is a real number b can't be infinity
infinity isn't in the set of reals or the natural numbers

real numbers are a set of (-infinity to infinity)
and natural numbers a set of (1,infinity)

reals: (-infinity, infinity)

infinity is not a definite value like 1 or 2 or 3 ita a hypothetical term with no end hence the open bracket, but by saying real numbers lie from -infinity to infinity you refer to the fact that they can have "anyvalue possible" and if u say b=infinity u refer to the fact that b in reality is a value that cant be really defined hence the term "not defined" is commonly used, what i mean to say is when some one says b=infinity what they really mean is that its not defined,and do not refer to b having a definite value.

hope that clarifies your doubt.

For all b =/= 0 yes. This statement is true

That statement is true even if b=0, brainlet

0/0 = 0 ? who's the brainlet here