As the other number the Zero, Infinity is not basically defined in mathematics as people did not have a notion of either in the past. They just got into the mathematics from the foreigners. But in wikipedia it goes like this:
"Infinity (symbolically represented with ∞) comes from the Latin infinitas or "unboundedness." It refers to several distinct concepts (usually linked to the idea of "without end") which arise in philosophy, mathematics, and theology.
In mathematics, "infinity" is often used in contexts where it is treated as if it were a number (i.e., it counts or measures things: "an infinite number of terms") but it is a different type of "number" from the real numbers. Infinity is related to limits, aleph numbers, classes in set theory, Dedekind-infinite sets, large cardinals,[1] Russell's paradox, non-standard arithmetic, hyperreal numbers, projective geometry, extended real numbers and the absolute Infinite"
Still lacking the basicness of it init? Like it is defined based on so many others which started to exist only after in logic.
Scientifically: Infinity is the state when you start from Zero and keep on increasing all the harmonics of all the vibrations (space/time), until you reach a state they all cancell eachother out and become Zero.
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