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This is a follow-up to the question, What is the smallest possible positive number on an 8-segment array? However, this time repeats are allowed!

You are provided with the 8-segment array in the picture together with all the necessary electronics to make any combination of lit segments you want.

enter image description here

Fillable version for graphics http://i.stack.imgur.com/K1hnN.png

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What is the largest positive number that you can display? Unlike in the previous question, boxes can be identical. (A box is a grey rectangle containing 8 segments)

Any combination of segments is allowed within a box provided it is accepted by the community as a valid symbol. ('accepted' is decided by net up-votes for your answer)

Any recognised numbering system that is commonly used is allowed. If the one you use is common but little-known (perhaps because it is specialized) then you must back up your claim with a link to an authoritative source. You must also explain it precisely so that it can be understood by others.

You cannot mix numbering systems unless you can show that this is routinely done by some substantial section of the populace.

You cannot invent your own symbols or language. All symbols must be understandable and approved by the community.

The competition remains open until there has been no answer for one week. At that point (or as soon after as I am able) I shall accept the most up-voted answer (net votes).

Update

  1. If the question gets closed (and then possibly reopened) then I'll make an adjustment about the timescale for accepting an answer.

  2. If I could wind back the clock, I would require the answers to be finite. This was an oversight because I did not think an infinite could be considered a number.

  3. Because there are answers and they have been voted on, it is too late to change the criteria. My suggestion is that people who are interested submit answers in the categories of finite or infinite numbers according to their preference. I will stick to my original criterion for acceptance.

Note

You can display your answer using ASCII text provided it is clear how it would look when translated into segments. Otherwise please use an actual 8-segment representation to clarify the layout of any symbols that aren't obvious.

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    $\begingroup$ Most upvoted answer is almost certainly not going to be the "correct" answer. Your scoring condition makes this not a puzzle. $\endgroup$ – Deusovi Oct 30 '15 at 13:14
  • $\begingroup$ Here is a definition of puzzle. "b : a question, problem, or contrivance designed for testing ingenuity" merriam-webster.com/dictionary/puzzle -- I think I have complied with that. $\endgroup$ – chasly from UK Oct 30 '15 at 13:58
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    $\begingroup$ Because of the upvote metric, this question just tests how well you can get other people to upvote you. It may test ingenuity, but I don't think it's a puzzle. $\endgroup$ – Deusovi Oct 30 '15 at 14:15
  • $\begingroup$ @Deusovi, In that case I define this to be an open-ended puzzle that tests people's ingenuity in getting up-votes. The medium for doing this is a mathematical one. $\endgroup$ – chasly from UK Oct 31 '15 at 12:20
  • $\begingroup$ By that definition nearly everything is a puzzle. Is poker a test of ingenuity in getting people to believe you have a good hand? Is an exam a test of ingenuity of guessing what the teacher wants you to respond? You could technically say yes, but that doesn't make them puzzles. $\endgroup$ – Deusovi Oct 31 '15 at 15:43
4
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Using actual digits (instead of letters or concepts), I present

enter image description here

or $9^{11111111111111}$

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  • $\begingroup$ That reminds me of $9 \times 60^{-14}$. Since $9'$ is $9/60$ (9 minutes), $9''$ is $9/3600$ (9 seconds), etc. $\endgroup$ – Joe Z. Oct 30 '15 at 21:15
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    $\begingroup$ i.e. the number is $9''''''''''''''$. $\endgroup$ – Joe Z. Oct 31 '15 at 20:43
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If we're restricted to finite numbers, I submit...

enter image description here

ggggggg9.

That's the (((((((9th number in Graham's series)th number in Graham's series)th number in Graham's series)...)))) where Graham's series (notated as gn for some n) is defined under "definition" here.

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  • $\begingroup$ That's quite big. $\endgroup$ – chasly from UK Oct 30 '15 at 11:04
  • $\begingroup$ @chaslyfromUK: Yep. No idea why this was upvoted but aleph-999 wasn't though. $\endgroup$ – Deusovi Oct 30 '15 at 11:09
  • $\begingroup$ Maybe because this is finite? $\endgroup$ – chasly from UK Oct 30 '15 at 13:20
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    $\begingroup$ You could make it a little bigger by using two single segments in the last box to make an 11. $\endgroup$ – GentlePurpleRain Oct 30 '15 at 18:39
  • $\begingroup$ Is this number bigger or mine [tree(99)]? I don't know enough maths to figure it out. $\endgroup$ – ghosts_in_the_code Oct 31 '15 at 3:43
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I submit

enter image description here

ALEPH 999.

It's infinite, 998 'steps' above countable infinity.

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  • $\begingroup$ Hmm... Is that a number though? I don't think it is. Maybe I should have specified 'finite'. Let's see what the voting says. $\endgroup$ – chasly from UK Oct 30 '15 at 10:34
  • $\begingroup$ @chaslyfromUK: Yes, it is. It's part of the cardinal number system. $\endgroup$ – Deusovi Oct 30 '15 at 10:36
  • $\begingroup$ I think I need convincing. Can you show me a link where it is defined as a 'number'? $\endgroup$ – chasly from UK Oct 30 '15 at 10:38
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    $\begingroup$ Darn it. Let's see if anyone can beat it. (And there was me thinking a googol was big!) $\endgroup$ – chasly from UK Oct 30 '15 at 10:42
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    $\begingroup$ "ALEPHG64" is another solution that sort of works. $\endgroup$ – Joe Z. Oct 30 '15 at 21:14
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enter image description here

TREE(99) from Kruskal's tree theorem.

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As someone has submitted an infinite number, I'll kick off with a finite one which is pretty big.

1 GOOGOL

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P.S. I'd also offer 9 GOOGOL but I don't know if I would need an 'S' on the end.

EDIT

Or 99GOOGOL if I am allowed to omit the space.

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  • $\begingroup$ The quotes arouns "number" are unnecessary. $\endgroup$ – Deusovi Oct 30 '15 at 10:52
  • $\begingroup$ You don't need an S at the end c: $\endgroup$ – Deusovi Oct 30 '15 at 11:00
  • $\begingroup$ Do I need a space between the digit and the G? $\endgroup$ – chasly from UK Oct 30 '15 at 11:00
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    $\begingroup$ I think it's okay to not have that space for a 7-seg display. $\endgroup$ – Deusovi Oct 30 '15 at 11:01
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    $\begingroup$ 9eGOOGOL maybe? $\endgroup$ – Dennis_E Oct 30 '15 at 11:05

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