Infinity can't be a constant because ∞ ± k = ∞ , but a constant changes (its) value when something is added or subtracted.
But infinity can't be variable because the definition of variable is
"A variable is a symbol that stands for a value that may vary" or stating in simple terms
"In mathematics, a changing quantity (one that can take various values) is variable"
But infinity is not defined, so it can't vary with wrt to anything.
so infinity is just a concept and it is not a real number
so ee cant say it as a variable or a constant
Try to understand the concepts.
like if u r satisfied with the explanation