Does infinite time really equal infinite possibilities?

the true answer is NO, let me explain:

the answer is yes, but in order to satisfy your premise stated in your question, the true answer must be no, because in order for everything to be a possibility, its impossibility must also be included, understand?

Let's assume, for a moment, that you're trying to understand reality and not simply debate things that lie outside of it.

Infinite time in a perfect cyclical system invariably ends up representing the path(s) of least resistance (of equal values) between infinitesimal contraction (or enthalpy) and infinite dissipation (or entropy) which I call the possibility-space. The same infinite time, in a permutating cyclical system, ends up representing all paths of least resistance of any value in the possibility-space. As for infinite time in a non-cyclical system, it merely remains unstable and thus cannot possibly exist. Nothingness is absolute, it is everything outside of reality, but it can only ever take shape (become real) through the bottleneck that is probability-space -- which also called necessity or commonly described as a deity.

Existence itself, or reality, is defined by movement performed linearly (in either direction) along any given path of least resistance in the probability-space. The only unique aspect about consciousness is its impact on the overall system: it increases and alters the final expression of the first and second laws of thermodynamics.

Please do note that these thoughts imply that the purpose of morality and life itself is the maximization of, and control over, the expression of entropy and that all of this implies the impossibility of true death or in-existence, if only because nothingness (which is ironically also everything-ness) is all-pervasive and so is the probability-space.

Also, exponential economic growth combined with limited resources (energy) isn't sustainable and all capitalistic economies will thus clash with the nature of reality and the reality of nature.

Hopefully I've answered (some of) your question(s).

If you are talking random possibilities, then yes, infinite time (at least theoretically) allows infinite combinations. This assumes the combinations are physically and logically possible to begin with.

But, the problem is that time began at the Big Bang some 13.72bya. There is no reason to consider time infinite.

I don't think so. There's always an influence....potential at work that determines other behavior or reactions IMHO. Everything doesn't have an equal chance because of prior influences. That helps determine the scope of the next progressive 'occurrence'. That's why I don't believe a group of monkeys given an unlimited amount of time could complete the works of Shakespeare. I don't think anyone considers that they might just pound on the same 8 keys the whole time.

Time is a dimension.

It is relative to a frame of reference.

Most abstractly time is simply mutability across two or more frames of reference.

In order to establish the concept of time there must also exist constants.

Complete mutability across two given frames of reference will not establish any concept of order.

Without a constant to ground your frames of reference within some semblance of rationality...you would be unable to perceive the concept of time.

Constants across two or more frames of reference should not be considered unique instances, but indeed be considered recursions.

So drawing from your example any two frames within the string t=630471374336a+1e

Any two units of second that are compared and do not result in an a and an e, would become an example of an a recursion.

Anyway what you describe reminded me of the diagonal method in set theory.

Very unique intellectual answers....

All things are possible...

Just where does the intellect end?

"Wisdom" declares that time and space both end for one, precisely when one exhales ones final breath.

Time is not infinite...

Space is not infinite...

However the One that created both time and space, is indeed infinite!

All one must do within ones life span, is "Remember".

Peace be always with you.

in sha'Allah

al-hamdu lillah

Salaams,

If it is one or the other that must be for any moment given, then for any discreet partition of time passing, there are infinite momenta orderly perfilled by an infinite progression of this's and that's

I don't see why not

yes, for all practical purposes, but only if your definition of infinite time includes moving "side-ways" through time into alternate timelines and infinite probable versions of this very moment.

Yes, but "don't let time catch you sleeping"