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1d
comment Are the Real numbers really Complete?
@chharvey The two properties I mentioned follow immediately from the Conway style definition (equivalence classes of pairs of sets of surrreals). And if you meant more reading about the surreals in general, there's way too much for me to put in this comment. If you're looking for a specific flavor of treatment and can't find it, maybe email me and/or post a new question.
1d
comment Can a number have an uncountably infinite amount of digits?
The examples at that mathoverflow link aren't really sets where someone does something like use more than countably many digits, because nothing like digital expansions really arise. That said, sign expansions of the Surreal numbers (or a field naturally sitting inside) are pretty close to binary expansions which can involve a an expansion of uncountable length.
Jul
29
comment Notation for polynomials and equating coefficients
Can you name the paper? Without context or an example of what the paper means by this notation, I'm not sure what "given $t$" should mean.
Jul
28
comment Permutational Question
I misread the question. Your interpretation is very likely correct. Good work.
Jul
28
comment Permutational Question
AB, AC, BA, BC, CA, CB are the six permutations of two distinct letters from {A,B,C}. Could you clarify what you're unsure of?
Jul
28
comment On a metric over m-subsets of [n]
I would say this metric is just the Manhattan Distance in $\mathbb R^m$ restricted to a very special domain.
Jul
27
comment Clarification of definition of “inverse” with quaternions
Quaternion multiplication is not matrix multiplication of the corresponding vectors, as that's undefined.
Jul
27
comment The set of all real functions of a real variable
If you can argue that $\mathfrak{c}^{\mathfrak{c}}\ge2^{\mathfrak{c}}$ then that's enough. I'm not certain where the "$2^{\aleph_0 \mathfrak{c}}$" is coming from.
Jul
20
comment Can we generalize Aleph numbers to non integer values?
I don't think there is any natural way to extend $\aleph$ to non-ordinal inputs in the surreals. Since by definition $\aleph$ makes a sort of huge jump with each successor, I have no idea what, if any, would be an appropriate way to interpolate. Certainly you could interpolate linearly or any other way you want, but I doubt this can lead anywhere satisfying.
Jul
12
comment example of multiplication of ordinals with infinite cardinality with larger value on right where we dont' take the max?
Cardinal arithmetic has addition and multiplication with an infinite cardinal reduce to max. See en.wikipedia.org/wiki/Cardinal_number#Cardinal_arithmetic (There the only case you have to watch out for is multiplication by $0$.)
Jul
11
comment Is Wolfram wrong about unique 3-colorability, or am I just confused?
Has anyone informed the website maintainers about the error?
Jul
4
revised Pseudo-Surreal numbers are analogous to?
added tags
Jul
4
answered Pseudo-Surreal numbers are analogous to?
Jul
1
comment Examples of calculus on “strange” spaces
Maybe you're looking for the term "derivation" in the sense of abstract algebra? Maybe you'd be interested in en.wikipedia.org/wiki/Arithmetic_derivative ?
Jul
1
answered Decoding the sign expansion of surreal numbers
Jul
1
comment Unusual result to the addition
@rogerl It's worth noting that that expression for a sequence of 1s can be found as an application of the formula for the sum of a finite geometric series.
Jul
1
comment Rational Irrational Numbers
As an aside, you may be interested in reading about continued fraction representations of numbers, where irrational solutions to quadratic equations with rational coefficients (like $\sqrt2$) have repeating expansions, but other irrationals don't.
Jul
1
comment “On Numbers and Games” or “Winning Ways for Your Mathematical Plays”?
I read those two simultaneously, but I would recommend Lessons in Play as a starter book over either of those. It's more accessible to an undergrad and generally clearer about theorems and proofs, for the most part. After that, if you want to read heavier/broader theory, Combinatorial Game Theory by Siegel would be a good option (covering essentially all of the theorems from ONAG and WW), but it doesn't have too many examples, being a graduate textbook.
Jun
19
comment Is there such a thing as “quadratic independence” (and higher generalizations of linear independence)?
Aside from algebraic independence, the other thing that comes to mind is the concept of "matroid", which is the sort of abstract general structure linear independent sets of vectors have.
Jun
18
answered Summation functions for wall clock, 10AM, 11AM and 12PM tips needed