🔔 SHAME 🔔

was that guy Socrates or perhaps Einstein

Infinity. Checkmate.

I dunno about proving you wrong, but the fact that you can comfortably say there is no largest natural number is kind of a belief in infinity

Might be this? https://en.wikipedia.org/wiki/Absolute_Infinite

Or this is about some people thinking infinity is just a really big number, with which you can do calculations like e.g. (these are non-sensical!):

• ∞ - ∞ = 0
• 2*∞ > ∞

There are different kinds of infinity

"Countably infinite" means an infinitely-large set of numbers that could be generated by infinitely following an algorithm with a finite number of steps. For example, natural (positive whole) numbers are countably infinite because they could be generated by following this simple algorithm:

1. Start with the number 1
2. Add 1 to your number
3. Repeat step 2

The set of real numbers, on the other hand, is uncountably infinite because you can have an infinite number of digits after the decimal place. You can't define a finite generation algorithm like the one above simply because any precision you use wouldn't cover the full range. In other words, if you wanted to modify the above algorithm, and chose 0.1 as your starting number, your algorithm would miss 0.01. If you chose to start at 0.01, you would miss 0.001, and so on

IMO? That infinity is just a concept to occupy professional thinkers that breaks every construct wherein it's applied.

I'm not sure anyone has really provided a complete explanation of what is the difference between working with an absolute infinity and the way we do math normally in science and such.

Basically, no one has found the idea of using an absolute infinity to explain the world to be better than the way we deal with infinity in college courses. In college, you run across the idea that some infinite sets are larger than others (countable numbers vs uncountable). Edit - I think you could have the idea of different sized infinities and a final largest absolute infinity. It’s just that this concept isn’t useful. It would be like claiming God is purple. Nobody can prove you wrong and it doesn’t matter.

Of course, an infinite set makes sense in math, and has practical uses in the sciences, but nothing can truly be demonstrated to be unending. Another poster put it nicely - infinity is a direction, not a destination.

I recommend this video How to count past infinity by Vsauce (about 20 minutes long). It is closer to entertainment than a lecture but its pretty good. I'm only an undergrad math major but I haven't found any real problems with this video (though, he does start talking about ordinal numbers which aren't terribly useful to anyone that I know of, yet, except for some really complicated number theory stuff cryptographers might use, don't ask me. cryptographers are basically wizards imho).

The question doesn't make sense, there are many things which have an infinite quality (like infinite cardinality) or are called infinite/infinity (like infinite cardinals and ordinals). They're not contradictory. They coexist the same as all finite things do.

There is currently no way to observe any of this empirically, so the question is pretty much moot. It's speculation either way.