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I recently posted a question about numbers. I was thinking that it was a legitimate question. Maybe I didn't ask it well, but I saw similar questions (such as Does Pi contain all possible number combinations?). My question is:

Is there a number so large that we could never calculate it?

I wasn't sure if there was an answer or if there is any information or if anyone even asked this question before… But I was really curious about it. Now I regret asking because I feel most of the people think my thoughts are just stupid (someone even referred to some program for children), but I like a couple of the links I was given.

Is there something wrong with my question? Should I delete it?

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    $\begingroup$ Personally I don't think there is anything wrong with the question. I can answer it, I think. I've voted to reopen and I hope at least four others will do as well. $\endgroup$ – wythagoras Jul 24 '15 at 14:14
  • $\begingroup$ I think the question should be re-opened. For now, I've posted an answer there as a pair of comments. My answer presumes that you want not only to calculate a number, but that you also want to know that you've calculated it -- i.e., a computation together with a proof of correctness. $\endgroup$ – r.e.s. Jul 24 '15 at 14:26
  • $\begingroup$ Speaking only for myself, I think it's a perfectly valid question for a math Q & A place like this. $\endgroup$ – Bob Happ Jul 27 '15 at 20:35
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Having looked at your question, I think that some of the commentary was a bit harsh (luckily I can fix that). I also felt that the chosen close reason (chosen by four of the five close-voters) wasn't appropriate. Were I to have voted, I would have chosen unclear what you're asking because, well, it's unclear exactly what you are asking. (The fifth close-voter chose this option.)

Your main question is

are there numbers that are just too large ... that we can't write them down in any way at all that expresses their exact value?

This leaves a lot to be interpreted. What do you mean by "write them down in any way"? And how should one writing "express their exact value"? I would assume that a number's decimal representation expresses their exact value. But what about the following?

$\operatorname{TREE}(3)$ where $\operatorname{TREE}(k)$ is the maximal length of a sequence $T_1 , \ldots , T_\ell$ of $k$-labelled trees where $T_i$ has at most $i$ vertices, and no labelled tree embeds as a minor (together with its labeling) into a later labelled tree in the sequence. (See the Googology Wiki.)

This gives a definition of a unique number, but really doesn't help in determining much about the number. (Well, it does make Graham's number look like an infinitesimal, but that's not exactly immediate.) Would this be a way to write down a number in a way that expresses its exact value?

What you mean by these really affects what the question is, and what suitable answers are. There might be an interesting semi-philosophical question here, but as it stands I'm not certain it can be appropriately answered (hence, I feel it is unclear).

If you don't feel that you can make it more clear, then deletion is an option, although if it doesn't get re-opened it will likely be a candidate for automatic deletion.

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  • $\begingroup$ Completely off-topic, but I don't understand why $T_1$ (the tree with one vertex) would not embed in the following trees... $\endgroup$ – Najib Idrissi Jul 24 '15 at 11:23
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    $\begingroup$ @Najib The embedding has to respect the labeling. So, in particular, whatever label the unique vertex in $T_1$ is given, no other vertex in any later tree can be given that label. $\endgroup$ – user642796 Jul 24 '15 at 11:47
  • $\begingroup$ Thank you very much for your full response. I'm not always good at expressing the questions I have, but I didn't realize it was that ambiguous. I tried to at least make it somewhat specific so that I wouldn't get an answer like "Let x be a number. Let x go to infinity" or something like that. It is difficult to explain my thoughts here. Other than a "trick" like the limit I gave, I feel like there must be numbers that are simply too big to ever calculate or express. I'm not sure how else to ask this and I'm considering closing the question. $\endgroup$ – zagadka314 Jul 24 '15 at 15:57

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