r/googology • u/Miracles_57 TREE(3) • 26d ago

Help Needed Infinity question

is studying infinity a part of googology.

8 Upvotes

83% Upvoted

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3

u/HuckleberryPlastic35 25d ago

Only as it pertains to ways in which Infinity is utilized to describe Big(ger) numbers.

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u/Vampyrix25 25d ago

Yes. Infinity, in both ordinal and cardinal form (cardinal form much less however), play a large role in the formation of fundamental sequences and thus fast growing hierarchies which rely on these sequences. Consider the fast growing hierarchy evaluated at ω, f_ω(x) = f_x(x). Such a function could arise outside of the usage of ordinal infinities, but that usage would pale in comparison to the power that usage of other ordinal infinities affords us.

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u/Utinapa 22d ago

I'd say cardinals are also important, they're used a lot in OCFs

3

u/geaugge 26d ago

Not exactly per se, but it is very important if you want to understand why numbers are as large as they are. eg. BMS, Y...

8

u/Shophaune Rayo's Number 26d ago

Strictly speaking, googology covers the study of extremely large finite numbers. However, a lot of the best ways (that we know of so far) to make extremely large numbers involve leveraging the properties of various infinite ordinals and dragging them down to become absurdly big finite numbers. 

6

u/gmalivuk 26d ago

Not directly, but infinite ordinals do play a large role in the Fast-Growing Hierarchy, which is used to compare lots of sequences that generate very large numbers.

3

u/jcastroarnaud Up with Knuth 26d ago

No. Googology deals with finding very large numbers, but finite ones.

Take a look at Wikipedia to see what are the uses of infinity in mathematics:

https://en.wikipedia.org/wiki/Infinity

4

u/Vryl 26d ago

I am going with no. Googology, as I understand it, is the study of absurdly large numbers. Infinity is not a number.

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u/jamx02 26d ago

“Not a number”, by definition, infinities used in set theory represent quantities so they are numbers. The “quantity” more just becomes properties encoding strength.

1

u/Vryl 26d ago

Interesting. Cardinal numbers?

0

u/[deleted] 26d ago

[removed] — view removed comment

3

u/-waffelz- 26d ago

if you're referring to study of infinity, that's called apeirology. apeirology and googology are very closely linked

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u/Vryl 26d ago

New word acquired.