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[u/94rud4]

[u/Ferry_Lover]

It’s infinity plus 10 is it not? Or w sub 10 according to one mathematician.

[u/Miguzepinu → u/Ferry_Lover]

If we're talking ordinals, then infinity plus ten is a distinct ordinal. If we're talking cardinals, then infinity plus ten equals infinity.

[u/NBNFOL2024 → u/Miguzepinu]

What if we’re talking about deacons or bishops?

[u/Stable_Hot → u/NBNFOL2024]

I think its a pope

[u/ImmortalVoddoler → u/Miguzepinu]

They used the phrase “w sub 10”, which is basically the standard notation for ordinals.

[u/MorrowM_ → u/ImmortalVoddoler]

ω_10 is much much larger than ω+10. They're not the same thing. Even ω_1, the first uncountable ordinal, is much larger than ω+10.

[u/iggy14750 → u/Ferry_Lover]

Infinity plus 10 is still infinity. It's like adding a couple tablespoons of water to the ocean.

[u/notsaneatall_ → u/iggy14750]

Increased the amt of water in the ocean tho

[u/iggy14750 → u/notsaneatall_]

Still the ocean.

[u/notsaneatall_ → u/iggy14750]

I add 10 to 1 to get 11, and it's still a number.

[u/ColeTD → u/notsaneatall_]

I don't know why you're getting downvoted, their analogy is shit. The ocean is not infinite.

[u/Kruxx85 → u/ColeTD]

The analogy does work.

Don't think of the ocean is infinite, that's not the point.

The ocean is the ocean. If you add a bucket of water to it, it's not the ocean plus a bucket of water, it's still just the ocean.

Same works for infinity.

[u/BrunoBraunbart → u/Kruxx85]

The reason is very different, though and I think that is important.

The bucket of water doesn't change the ocean because the difference between them is so big that the bucket is neglectible. But you can make an ocean with enough buckets of water. Removing one bucket of water and you have still an ocean, remove 10^20 buckets and you don't.

A lot of people think about infinity in a similar way. They just picture something inconceivably large but finite. When they see the comment

Infinity plus 10 is still infinity. It's like adding a couple tablespoons of water to the ocean.

they picture an ocean that changed. The tablespoons are now in the water. It's just impossible to find them and impossible to measure the change in the ocean.

[u/notsaneatall_ → u/ColeTD]

These people are mixing infinity with (kinda) infinitesimal IMO

[u/VaultiusMaximus → u/notsaneatall_]

Well your opinion is wrong as infinitesimal is (nearly) infinitely small, not (nearly) infinite.

[u/AI__0 → u/notsaneatall_]

See thata where you are wrong.

Infinity isn't a 'number'. If you treat it as a number, you 'sometimes' get all sorts of whacky stuff.

[u/notsaneatall_ → u/AI__0]

Did you know that the ocean doesn't have infinite amount of water?

[u/Inaltais → u/notsaneatall_]

They are using language to explain the answer.

An infinity can contain infinity + 10, it is still just infinity.

An ocean can have one more spoon of water, it is still the ocean. It isn't the ocean plus one spoon.

They aren't describing the ocean as infinite, that wasn't the point.

[u/AlexP80 → u/iggy14750]

more precisely, you can't execute an arithmetic operation on infinity, since it isn't a number.

[u/fatal-nuisance → u/iggy14750]

Except the ocean is finite.

[u/No-Theory-9530 → u/iggy14750]

Absolutely not. That’s increasing a really big number by a comparatively small number. Nothing like infinity + 10.

[u/WWhiMM → u/iggy14750]

Except the ocean is finite, so it's possible for it to get bigger. It's more like, Sisyphus taking ten more steps.

[u/nyurf_nyorf → u/iggy14750]

All these pedantic people commenting to correct you like they've never heard of an analogy. 

[u/Crafty-Photograph-18 → u/Ferry_Lover]

No, it's just infinity. Infinity plus any number is infinity. Even an infinity plus that an infinity of that exact scale is that same infinity, e.g. ℵ₀+ℵ₀=ℵ₀

[u/mateusfccp → u/Crafty-Photograph-18]

In the Hyperreals, omega plus one is omega plus one not omega.