Ordinal numbers - when you wonder what's the biggest number and say "infinity", or "infinity + 1", or "infinity infinities", mathematicians say "why stop there?"
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For those not familiar- there are different kinds, and “magnitudes” of infinity! Imagine “infinity.” You start a 1, maybe 0- and you just keep counting forever. Infinity right? Not quite. “Listable infinity.” But- if I have a table that is infinity- I can work across it in rows, columns, diagonals. We can even “cross” infinity to find within a random string of infinite numbers- infinite listings in sequence if all numbers or OUT of sequence all numbers which we can place into sequence- repeating infinitely.
Within sets of infinity we can find “countable infinity” and “non countable infinity”- we can find various sets of infinity- and sizes! If we lost infinity- smallest number to largest number- and start at the same time- infinity going “1,2,3...” is going to be larger in VALUE than infinity going by fractions like “1/24th, 1/12th” and so on- and infinity could go “backwards” starting at say- 1/24th and continuing to get infinitely smaller into billionths and far beyond!
We can also have sets of infinite sets, and even infinite infinite sets! So for those unaware- “infinity” is more complex than just being “infinite” and while it usually has limited to no practical application when we use the term- there are different sizes of infinities and we can compare infinities.
Infinity also has different uses! For example- “infinite” can define a variable without upper or lower limits- that would keep going with no known end. This is sometimes used in practical systems as a concept- where the variable is not ACTUALLY infinite- a computer for example would eventually, no matter how big we made it to our current technology, run out of space to add digits. Once we include decimal places in addition to whole numbers- we can have numbers with truly humungous numbers of digits required to represent even “small” numbers like “1.”
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(TITLE FROM REDDIT r/woahdude)