First, what is it?

infinite

[in-fuh-nit]

adjective

1. immeasurably great.

2. indefinitely or exceedingly great.

3. unlimited or unmeasurable in extent of space, duration of time, etc.

4. unbounded or unlimited; boundless; endless.

5. Mathematics: not finite. (of a set) having elements that can be put into one-to-one correspondence with a subset that is not the given set.

Origin of infinite

1350–1400; Middle English < Latin infīnītus boundless.

According to definition #1, there is a sense in which the infinite can describe merely what is not measurable, so in that light, finite amounts can be so large that they are not measurable, yet are still finite. This is not the sense that I intend to deal with when talking about infinity. Finite numbers that are so large that they couldn't be represented on the entirety of the observable universe, even if written on the planck scale, I'm defining those as "dark numbers" because they are finite, but unrepresentable (dark/unseen) within the universe.

Hopefully we can all agree that a good working definition of infinity is "boundless", "without bounds or constraints: either physical or conceptual".

Now, can the boundless exist? Well, what does it mean to exist? This dot exists ---> . because there is something that is not-dot providing contrast and context (the white background), so existence is the relationship of the dot to the not-dot because if either are missing, then there is no dot and no dot could be said to exist. Existence is therefore dependent upon relationship and relationship precedes concepts of existence.

Now, what if the dot had no boundary? Well, immediately we can surmise that it would have no contrast because if the dot had no boundary, there would be nothing that is not-dot to provide the contrast in order to underpin existence. And if there were something to provide contrast, then obviously the dot would have a boundary. So right off the bat we can say infinity isn't anything that can exist, but I'm just getting started.

Infinities are said to contain things, because they contain infinite things, but how can a container contain anything with no walls (boundaries)?

Infinities cannot have beginnings or ends because those are boundaries and we said in the beginning that infinity has no boundaries. We cannot divide infinity in half and say infinity is bounded by this finite location and extends to infinity in that direction; it's nonsense and breaks our definition of infinity being boundless. Zero is not a boundary, but is just an arbitrary starting point on an infinite number line extending in both directions and we could just as easily started at -2,-1,0,1,2,3,etc or 5,6,7,8,etc. A line that is not infinite is a segment because all lines are defined to be infinite within the construct of mathematics; therefore a line with a beginning (such as a timeline) is not an example of infinity. Further, if time had a beginning, infinite time could not be said to exist until forever arrived, and forever means never because forever can never be realized, so infinite time could never exist if time had a beginning.

A better conceptualization for eternity is absence of time instead of infinite amounts of it, but really they both mean the same thing since in both cases time would have no relevance.

Since infinity has no starting point/reference point/unique edge, then infinite computer memory would equate to having no memory and anything written to memory could never be found again. Where would allocation start? Afterall, the memory stick would take every bit of space in the entire universe because to say it wouldn't would be to limit the size of it. Where would an origin/center be placed and how could it be found again?

The infinite is the ubiquitous, omnipresence. If there were infinite oranges, then oranges would exist everywhere there is a place for an orange to exist which would leave no room for anything that is not-orange, and so by having an infinite amount of oranges, we have a non-existence of oranges since there is nothing that is not-orange to provide the contrast and underpin existence. Therefore, what is infinite is nothing and nothing is the only thing there can be infinite amounts of.

Infinity and zero are tied at the hip and every number has a pair: 1-1, 2-2, 3-3, etc. Every number has a negative partner, except zero, but the partner to zero is infinity and, conveniently, neither exist.

Here's more reading on the topic http://theorangeduck.com/page/infinity-doesnt-exist

Here's a debate involving N.J. Wildberger (Yale Phd in Mathematics and former instructor at Stanford and author with extensive youtube channel devoted to math):

Here is a video going into more detail about dark numbers:

Here are a couple youtube comments that resonated well with my sentiments:

Daniel Șuteu

This is like preaching atheism to mathematicians; I imagine in the future that mathematics will become a substitute for religions and religious discussions about the existence of a god will be replaced with discussions about the existence of very large numbers, like our z or its prime factors. I agree with you up to some extent only, and as I'm trying to agree more with you, something inside of me tells me that this does not feel right. The idea of continuity and the consistence of mathematics is quite contradictory with the belief that this rules does actually break up eventually. From a mathematician point of view, the universe is truly infinite in every regard. The limits are imposed by our finite reality, which I think it's only a projection of the true "reality". Nevertheless, understanding the limits of our projected reality can be something useful, as we all live inside it, an d it may give us more clues about the true reality that may or may not exist out there.

njwildberger

Your last phrase sums it up well: "the true reality that may or may not exist out there". Is this the kind of reality we want to consider? How about the reality around us, that we are sure exists, because we have direct evidence for it? How about the reality that our computers reveal?

I am preaching science rather than atheism, via an orientation based on clear definitions, explicit examples and concrete computations. I propose that we move towards a scientific approach to mathematics, not a religious one. Let's replace the abstract study of notions of what might be, with explicit investigations of what is actually here.

Belief in infinity is a religion, because there is no evidence for it and it must be assumed to exist on faith, and there is no arguing with religion.

If anyone has evidence that infinity exists, please post it below. Questions are encouraged, but dogma is not.