Talk:2966: Exam Numbers
pre-algebra: 4, calculus: pi^2 / 4 (about 2.467), physics: cosmological constant: depends on how you measure it 162.158.167.48 18:11, 31 July 2024 (UTC)
Game theory: -5x10⁶ (maybe helpful, maybe not... just be thankful I didn't include an i factor in there somewhere...) 172.70.162.185 18:20, 31 July 2024 (UTC)
- Interesting; I went with ∞+10. So, between our answers, that makes the average...
- ProphetZarquon (talk) 05:21, 1 August 2024 (UTC)
Could somebody reformat all the math here in whatever LaTeX plugin this wiki uses? --162.158.222.102 18:35, 31 July 2024 (UTC)
- Probably not, because the MathML here is broken. But, also, nothing I see requires anything particularly complicated, it can all stay in fairly straightforward (standardly formatted) text. 141.101.98.224 18:44, 31 July 2024 (UTC)
I had to look up "TREE(3)." Seriousness aside, I think the largest number would be the astrological sign 1 that has its end_points_ as galaxy clusters. 172.68.245.184 19:26, 31 July 2024 (UTC)
- Which astrological sign? Search engines aren't helping. Onestay (talk) 20:41, 31 July 2024 (UTC)
- The nonexistent one I just made up that looks like a "1." 😃 172.71.222.6 21:06, 31 July 2024 (UTC)
- 'OAK'? 'ELM'? 'ASH?' 'BOX'? 'YEW'? 141.101.98.165 08:52, 1 August 2024 (UTC)
If infinity _is_ a number, it might be a possible solution to the game theory question. The average of any set of numbers that includes infinity is infinity, and infinity + 10 is still infinity. I probably wouldn't try that in most classes, but a game theory professor might approve "gaming" the system, as it were.
- If I would prefer no-one (else) to win, I might submit -∞ as my answer. 172.70.90.74 20:13, 31 July 2024 (UTC)
- If I really wanted to mess with them, I would submit i. 172.70.160.248 08:54, 1 August 2024 (UTC)
I did a bit of a deep dive into wikipedia and the googology wiki and the answer to the last question depends on a few things (along with assuming ZFC). If transfinite ordinals count as numbers, then those at the end of List of large cardinal properties take the cake (if i'm reading it right). Otherwise, something based off Rayo's number is the best googologists have come up with so far. 172.69.246.149 20:18, 31 July 2024 (UTC)Bumpf
Isn’t the joke in the pre-algebra that it would require algebra in order ro calculate? 172.68.70.135 20:36, 31 July 2024 (UTC)
- Yes. I agree that it would be worth adding wording along the lines that “the joke here is that you need algebra to solve the equation”. Dúthomhas (talk) 20:56, 31 July 2024 (UTC)
- I interpreted the 'pre-' bit as being more like 'proto-' - i.e. it's not fully proper algebra, but it's the kind of work you would do in preparation for tackling proper algebra.172.68.186.156 08:58, 1 August 2024 (UTC)
You know, formatting math on this wiki would be a lot easier if the Math extension were correctly installed, but evidently it's not: Failed to parse (Missing <code>texvc</code> executable. Please see math/README to configure.): \int_0^\pi x \sin^2 x \;dx Zmatt (talk) 22:22, 31 July 2024 (UTC)
Is that integral really correct? I asked Wolfram Alpha and it gave me
- integral x sin^2(x) dx = 1/8 (2 x (x - sin(2 x)) - cos(2 x)) + constant
which does not seem to be the same as
- −2x sin(2x)+cos(2x)−2x)/28 + C.
But maybe there's something with half-angle formulas that makes them the same? … but I don't think so, they don't evaluate the same for x=0. JohnHawkinson (talk) 02:56, 1 August 2024 (UTC)
- Yup, looks like it was supposed to be
- -(2x sin(2x)+cos(2x)-2x^2)/8
- but they messed up the places of the negation and square.
- Though the important part here isn't what it is at any f(x), but what it is for any f(x)-f(y). In this particular case, f(pi)-f(0). 162.158.41.121 04:49, 1 August 2024 (UTC)
What is a number?
Infinity is _not_ a number. Dúthomhas (talk) 19:39, 31 July 2024 (UTC)
Infinity is absolutely not a number, and is the one answer I would mark as unambiguously wrong for the last one. Just say TREE(G_64) or something. 162.158.154.31 20:15, 31 July 2024 (UTC)
- This is correct. No one in post-grad math would write “infinity” and expect that answer to work. Infinity is NOT a number except for seven-year-olds. Yet the explanation above continues to posit it as a possible correct answer. Dúthomhas (talk) 20:49, 31 July 2024 (UTC)
- I qualify as a "post-grad math", and yet, I think infinity would have been a perfectly valid answer. Let me explain. The term "number" without further context is a bit vague, because there are several possible generalizations of natural numbers (something that presumably everyone agrees to call a "number"), and they are not compatible, ie. there is not a single generalization that generalizes them all. So we have to choose which generalization makes sense in the current context. Since the question is about thinking how big a number is, I naturally thought that the adequate generalization would be one that focuses on the order on natural numbers, ie. ordinals. In that case, my answer to this question would be "the class of numbers I can think of is not bounded, therefore there is no such thing such as a 'biggest number I can think of'". But if I had to write down a big number, I would write ε_{ε_{ε_{...}}} up until I filled the page, because that's the most efficient way I know to write a big, *big* infinity. Which is a number. (and I'm not seven, just to be clear) Jthulhu (talk) 08:35, 1 August 2024 (UTC)
- In IEEE floating point math, Infinity is not Not A Number. The latter is an indication of error (in a context where errors can't be signalled immediately) and an entirely separate concept to infinity. But both are not Normal Numbers. Or even Denormalized Numbers. Floating point math is a whole lot trickier than it appears to be at first glance, and only extremely tangentially related to mathematical reals. --172.68.205.54 00:48, 1 August 2024 (UTC)
A number, by definition, is a construct used to classify and/or compare values. How rigorous this needs be for one limits the extent to which they accept things as being a number. Even things like "apple" could be interpreted as (dimensioned) numbers, with a possible value being "1 fruit"; In that regard, one may consider things like apple=orange<grapes.
Just "infinity" is nearly useless in this regard, as it's "no end thing". Usually interpreted (when necessary) as the countable infinite cardinal x=aleph_null, this prevents most useful comparisons, including dimensional analysis since x^n=x for all counting (aka. finite positive integer) n. Spacetime may or may not be boundless, but we can't tell how many edges may or may not loop. Is it infinity? Yes. Is it infinite? God only knows. Can you *count to it*? God can. Does that make it a number? Depends. Is "infinity plus one" a sane concept? No, it can't be finite, ordinal, and/or real in a way addition is defined; It's without end, and if you could add to it, that would indicate an end.
In contrast, classification has its roots in trade, and barter, and tipping. How much of a thing is enough, but not too much. Somebody may accept between 1/2 and 2/3 of a pie you're splitting, because less wouldn't be fair and more may give them a stomach ache; Is 3<=6x<=4 a number? It's similar in uselessness to "infinity", but whether something is less or more can at least still be established within its range. In the limit, Surreal numbers are the principal example of classification, taking the arithmetic mean of the maximum and minimum of their lower and upper bounds, or the predecessor or successor, or zero. For example, y={y|1} is the biggest number less than one, with z<=y<1 for all z<1. It's less than one, but not any "smaller" than one, with an immeasurably infinitesimal difference 0<1-y.
Choice of axioms is very important for all this, since its full extent can render everything except finite non-negative integers "not a number" (by Presburger Arithmetic), or allow everything up to and including unique antichain cardinalities (by Martin's Maximum).
The sixth power of the smallest ordinal with the cardinality of the continuum in the constructed universe (w_1^6 where beth_n=C(w_n)) is the biggest number I can personally conceptualize, although I can consistently work with w_2 in this system as well. Does the fact that this is infinite make it any less useful as a number than 2.5? No. It says I can think accurately about all the standard ways of comparing things in up to 6 infinitely divisible dimensions. Just because one cannot necessarily picture something others can't doesn't mean it doesn't exist. If a one-eyed person can only see a 2 spatial + 1 temporal dimensional image, that doesn't mean depth doesn't exist, it just means it's "hidden" from that perspective. 3+1+2 has two "hidden" dimensions compared to normal 3+1 spacetime, and beth_1 is infinitely divisible unlike the quantum (at most beth_0) nature of our known universe, but I can still work with 3+1+1, and 3+1+2 in the same way people can think about a (possibly looping) universe where everything can be bigger or smaller, and spatial geometry itself may be some degree of spherical, and people have been working with fractions since antiquity, so why should I limit myself to what other people can grasp?
In summary: "number" is too vague for claiming most things "aren't" to be reasonable. Infinite values (that aren't just "infinity", that's vague enough by itself to be almost as unreasonable) are just one one example of a valid answer most people seem to be up in arms about. 162.158.41.181 01:06, 1 August 2024 (UTC)
- All right, all right. I yield. That’s some... _impressive_ reasoning. If we are going to redefine words to meaninglessness then there is no hope of engaging in useful discussion. I’m sure Randall will at least get a good laugh out of the idea that post-grad math students would submit “infinity” as the largest number they could think of. I still think it a disservice to readers to posit infinity as a _valid_ answer, though. Dúthomhas (talk) 05:05, 1 August 2024 (UTC)
