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1) If x is a real variable, then, is it correct, or is it acceptable rigorously to assign x

x = +infinity

?

2) if x is not necessary a real variable, then is it correct, or is it acceptable rigorously to assign x

x = +infinity

?

I am guessing the first one is wrong, because if x is an element of the real number set, then infinity is not an element of real number, so an unknown x can never be written to be equal to infinity.

I think the second statement is correct, because if x is not necessary an element of real number set, then it is correct to write unknown x is equals to infinity.