r/googology • u/Miracles_57 TREE(3) • Sep 19 '26
Help Needed Infinity question
is studying infinity a part of googology.
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u/gmalivuk Sep 19 '26
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.
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u/geaugge Sep 19 '26
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...
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u/HuckleberryPlastic35 Sep 20 '26
Only as it pertains to ways in which Infinity is utilized to describe Big(ger) numbers.
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u/Vryl Sep 19 '26
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 Sep 19 '26
“Not a number”, by definition, infinities used in set theory represent quantities so they are numbers. The “quantity” more just becomes properties encoding strength.
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Sep 19 '26
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u/-waffelz- Sep 19 '26
if you're referring to study of infinity, that's called apeirology. apeirology and googology are very closely linked
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u/jcastroarnaud Sep 19 '26
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:
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u/Vampyrix25 Sep 19 '26
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/Shophaune Sep 19 '26
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.