Forum:Theta

Forums: Index > Googology > Theta

What does \(\vartheta\) mean in, say, \(\vartheta(\Omega^\omega)\)? It's obviously an ordinal collapsing function but I haven't been able to find its definition. FB100Z • talk • contribs 18:03, April 4, 2013 (UTC)

I learned about gist of this function from Chris Bird's comparisons between ordinals and his separators. He doesn't defined it formally and explicitly but I understood how it works though. Ikosarakt1 (talk ^ contribs) 18:19, April 4, 2013 (UTC)

Can Deedlit or someone shed some light on this issue? FB100Z • talk • contribs 04:25, April 6, 2013 (UTC)

Hrm, is \(\vartheta(\alpha)\) is the least ordinal not constructible from 0, 1, \(\omega\), \(\Omega\) using addition, multiplication, exponentiation, the Veblen function, and previous values produced by \(\vartheta\)? This seems consistent with \(\vartheta(\Omega) = \Gamma_0\). FB100Z • talk • contribs 18:34, April 6, 2013 (UTC)

lol whoops, under this definition \(\vartheta(0) = \Gamma_0\) :P FB100Z • talk • contribs 18:40, April 6, 2013 (UTC)

Wrong. \(\vartheta(n)\) = \(\varphi(n,0)\) Aarex^Tiao 00:14, December 20, 2013 (UTC)

FB100Z already said that the definition doesn't match what we already know. You don't need to say that again. -- ☁ I want more clouds! ⛅ 05:27, December 20, 2013 (UTC)

there's a reason i wrote "lol whoops" FB100Z • talk • contribs 08:06, December 20, 2013 (UTC)

Why you writed "lol whoops"? Aarex^Tiao 22:09, December 21, 2013 (UTC)

Because he made a (fairly obvious) mistake. LittlePeng9 (talk) 22:13, December 21, 2013 (UTC)

@Aarex Sorry if this is a little harsh, but you seem to have an incomplete grasp of English. No worries, though, it's a tough language :| FB100Z • talk • contribs 23:05, December 21, 2013 (UTC)

Is :| emoij? This is Comment chain 7! Aarex^Tiao 15:27, December 22, 2013 (UTC)

@Aarex It's an emoticon.

@FB100Z You never tried to learn Polish. Each adjective can have freaking 100 forms, many of them different. English is extremelly simple compared to Polish. LittlePeng9 (talk) 21:13, December 22, 2013 (UTC)

1. Learn Polish Now! 2. Correct. Aarex^Tiao 21:51, December 22, 2013 (UTC)

@LittlePeng Holy crap. You weren't kidding 0_o FB100Z • talk • contribs 22:54, December 22, 2013 (UTC)

Continue the comment chain! Aarex^Tiao 22:56, December 22, 2013 (UTC)

aw yeah i found it FB100Z • talk • contribs 18:47, April 6, 2013 (UTC)

Actually, the definition in the article is for the \(\theta\) function (with two variables), not the \(\vartheta\) function (with one variable). I'll explain the differences between the various notations in a little while. Deedlit11 (talk) 03:08, April 8, 2013 (UTC)