Is the set of all real numbers x such that 0 < x ≤ 1, with operation multiplication.

Question

So I choose any elements x,y in the above set and considered their multiplication.

Since x and y are two different elements can their product be equal to 1? (Since if x = 1 then y cannot be equal to 1 right?)

So can we say the closure property holds for above set?

Thanks!

Answer 1

closure holds, but why do you say that x≠y? That is not necessary.

Answer 2

Isn't it required to show the closure property holds for two different number x,y?

Answer 3

closure means that if x and y are elements of the set, then x*y is also.
They need not be different.