Reputation
869
Top tag
Next privilege 1,000 Rep.
Create new tags
Badges
3 13
Impact
~16k people reached

16h
comment How is an empty set truly “empty”?
@ZevChonoles Okay, but in the bag analogy, this is actually a pretty reasonable distinction to make.
16h
comment How is an empty set truly “empty”?
I address this in the second section of my answer to the question you linked to: math.stackexchange.com/a/1256324/52057
Aug
26
comment Example of a number that is not the limit of a computable sequence
I am unfamiliar with all of the things you linked to, so I don't yet fully understand this answer. I'd like some intuition about what's meant by "arithmetically definable," though, if possible. Can you, for instance, determine the first several decimal-place digits of $\mathrm{Tot}$? The 30th? The $n$th?
Aug
26
comment Is 4 the second or third digit of pi
@JMoravitz I've always thought the most convenient stopping-point would be after "3.14."
Aug
25
comment What is meant by “finite algorithm” in Turing's definition of the computable numbers?
@JohnHughes Come to think of it, Turing claims in the addendum to his paper that using an alternate output schema (which of course necessitates a change in the algorithm schema) doesn't change the set of numbers that can be represented, except to permit negative numbers (for which the original schema didn't account). He doesn't really provide a defense for this claim, but it seems very close to an implication that the choice of algorithmic schema is irrelevant. On the other hand, that statement is too strong to posit without evidence, and it sounds quite similar to the Church-Turing thesis.
Aug
25
revised What is meant by “finite algorithm” in Turing's definition of the computable numbers?
deleted 251 characters in body
Aug
25
awarded  Self-Learner
Aug
25
revised What is meant by “finite algorithm” in Turing's definition of the computable numbers?
added 253 characters in body
Aug
25
comment What is meant by “finite algorithm” in Turing's definition of the computable numbers?
@JohnHughes Actually, I like that better. Thanks again.
Aug
25
comment What is meant by “finite algorithm” in Turing's definition of the computable numbers?
@JohnHughes Thanks; does the edit adequately address your concern? I suppose I've never seriously considered the implications of an uncountable collection of algorithm schemas, but I tend to suspect that $\mathbb{R}$ really truly does contain numbers with no algorithm in any schema. And possibly there is only a countable number of unique schemas....?
Aug
25
revised What is meant by “finite algorithm” in Turing's definition of the computable numbers?
added 26 characters in body
Aug
25
asked What is meant by “finite algorithm” in Turing's definition of the computable numbers?
Aug
25
answered What is meant by “finite algorithm” in Turing's definition of the computable numbers?
Aug
25
comment How are asymptotes actually defined in rigorous mathematics?
I like your "curve-free" definition, but I'm not sure whether asymptotes are commonly used (or even used at all) in modern mathematical research.
Aug
11
comment Do we need to formally teach the Greek Alphabet?
@JimiOke "We can do the same" meaning we can ensure that every kid has a "cool dictionary with a bunch of alphabets" in their house, which we assume that they will find and read?
Jul
28
comment Must all Lebesgue integrable functions really be invertible?
@IlmariKaronen Ah, thanks. I'd been wondering what the exact conditions were for those notifications.
Jul
28
comment Must all Lebesgue integrable functions really be invertible?
@FemaleTank Just making sure you get a notification for Cameron Williams's comment about accepting answers.
Jun
12
comment Express 99 2/3% as a fraction? No calculator
Beyond which, thinking about "mathematics" strictly in terms of algorithmic approaches to solving problems is entirely the wrong way to understand the subject.
Jun
12
comment Express 99 2/3% as a fraction? No calculator
+1. I disagree with the implication that you shouldn't try to do this as a math problem, but estimation and mathematical intuition are extremely valuable. Being able to work out something like this on pen and paper is actually not as useful or important as the ability to quickly see which solutions are reasonable.
May
23
comment Example of uncomputable but definable number
How does our knowledge that this sum cannot be computed prove that the number itself is not (coincidentally, and necessarily unbeknownst to us) computable via some other algorithm?