IMO? That infinity is just a concept to occupy professional thinkers that breaks every construct wherein itâs applied.
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Zoldyck@lemmy.world â¨2⊠â¨years⊠ago
Which theory is the most plausible?
xia@lemmy.sdf.org â¨2⊠â¨years⊠ago
Zoldyck@lemmy.world â¨2⊠â¨years⊠ago
Where and how does it end? Both infinity and non-infinity seem strange to me.
Ephera@lemmy.ml â¨2⊠â¨years⊠ago
Our mathematical definitions say that it does not end. Weâve defined addition so that any number + 1 is larger than that number (i.e. x+1 > x).
Youâre probably confused, because you think infinity is a concrete thing/number. Itâs not.
In actual higher-level maths, no one ever does calculations with infinity.
Rather, we say that if we insert an x into a formula, and then insert an x+1 instead, and then insert an x+2 instead, and were to continue that lots of times, how does the result change?So, very simple example, this is our formula: 2*x
If we insert 1, the result is 2.
If we insert 2, the result is 4.
If we insert 82170394, the result is 164340788.The concrete numbers donât matter, but we can say that as we increase x towards infinity, the result will also increase towards infinity.
(Itâs not 2*infinity, that doesnât make sense.)Knowing such trends for larger numbers is relevant for certain use-cases, especially when the formula isnât quite as trivial.
weker01@feddit.de â¨2⊠â¨years⊠ago
That is until you meet analysis people that define a symbol for infinity (and itâs negation) and add it to the real numbers to close the set.
Also there are applications in computer science where ordering stuff after the first infinite ordinal is important and useful.
Yea unfortunately we do kinda calculate with infinity as a concrete thing sometimes in higher level mathsâŚ
kogasa@programming.dev â¨2⊠â¨years⊠ago
Limits at infinity are one thing, but infinite ordinals are meaningfully used in set theory and logic
kogasa@programming.dev â¨2⊠â¨years⊠ago
The question doesnât make sense, there are many things which have an infinite quality (like infinite cardinality) or are called infinite/infinity (like infinite cardinals and ordinals). Theyâre not contradictory. They coexist the same as all finite things do.
Diplomjodler3@lemmy.world â¨2⊠â¨years⊠ago
There is currently no way to observe any of this empirically, so the question is pretty much moot. Itâs speculation either way.
urist@lemmy.blahaj.zone â¨2⊠â¨years⊠ago
Iâm 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).
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. Iâm only an undergrad math major but I havenât found any real problems with this video (though, he does start talking about ordinal numbers which arenât terribly useful to anyone that I know of, yet, except for some really complicated number theory stuff cryptographers might use, donât ask me. cryptographers are basically wizards imho).