Subduction Zone
Veteran Member
There are several different notions of infinity.
Infinity as a limit describes what happens to a function, and simply describes some variable getting larger and larger as some other variable does something.
Infinity as a quantity (known as cardinality) is a different notion of infinity. But, there are different sizes of such infinite quantities. The smallest such infinity is that of the 'number' of counting numbers (positive integers). The 'number' of decimal numbers is a larger infinity than this.
There are also ordinal concepts of infinity. Such can have either infinite ascent, infinite descent, or both.
There is no 'largest number', and no 'largest number before infinity'. And infinite sets need not have a 'start' nor an 'end'.
What happens here depends on the type of infinity. For limits, these equations are all correct.
For cardinals, a sum or product of infinite cardinals is the larger of the two. Exponentiation is a lot trickier. If you want an exposition, I will be happy to give one after I'm back from vacation.
For ordinal infinities, things get stranger.
Boundaries are a concept from geometry (or topology). Most versions of infinity are not in that context, so the notion simply doesn't apply.
Infinite in extent is different than having no boundary. For example, the surface of a sphere has no boundary, but is finite.
Dang beat me to it with the first example. But the OP asked if infinity had a beginning. The counting numbers do have a beginning at 1. They do not have an end.
I am unaware of other examples of infinity that have a beginning but not an end, but I have feeling that they are out there.