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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?
May
15
comment Is an irrational number odd or even?
As others have said, you cannot "prove" a definition; but you can use proof-like steps (induction and deduction) to motivate a definition, as in celtschk's answer.
May
5
comment Example of uncomputable but definable number
I don't actually believe, philosophically speaking, in non-computable reals.
Apr
30
comment What is an Empty set?
@BrianJ That's actually one of the most famous paradoxes in the development of set theory.
Apr
30
comment What is an Empty set?
@ruakh What CarlMummert said. Except that I would add that "<X> of real numbers" is terminologically more akin to "grocery <x>" than "<x> of groceries", despite the phrasing.
Apr
30
comment What is an Empty set?
The confusion of "how can a bag of shopping not hold any shopping" only (or at least primarily) exists because "hold any shopping" implies that the items usage, while "bag of shopping" could mean either usage. Hence why I clarified in my first response to you that a bag for shopping (the action usage) is always a bag for shopping, regardless of its contents. (Even if "for shopping" is taken to mean for holding shopping items!)
Apr
30
comment What is an Empty set?
@ruakh I say "slippery" not because it's "incorrect" English, but because the implied analogy to formal mathematical concepts makes no sense due to the multiplicity of meanings involved. If "shopping" means both the action of shopping and the items acquired while shopping, then it's not actually parallel to "groceries" or "holding", since "groceries" only means items and "holding" (in the D&D sense) only means the action of holding.
Apr
29
comment What is an Empty set?
@ruakh I guess so, but "bag of shopping" strikes my ears as something like a D&D-ism, and the noun usage of "shopping" seems a bit slippery. A bag for shopping is still a bag for shopping even when no shopping has yet been done with it.
Apr
29
comment What is an Empty set?
@Tom Depends what axiom schema you're using.
Apr
29
comment What is an Empty set?
@MadeleineP.Vincent Asking isn't sufficient; carefully considering the advice and feedback given on that forum is necessary as well.
Apr
29
revised What is an Empty set?
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Apr
28
revised What is an Empty set?
added 21 characters in body
Apr
28
comment What is an Empty set?
@SufyanNaeem I think my response holds even if you replace "help" with "help much." In any case, in my answer, I did my best to provide comprehensive answers to each of your questions; did that help at all?
Apr
28
revised What is an Empty set?
added 208 characters in body
Apr
28
comment What is an Empty set?
@SufyanNaeem No one's saying they "don't believe you"; they're just saying that if you're having trouble understanding that definition (and yes, not understanding why the empty set is a valid set means you're having trouble with the definition), then you should consider some other definitions, or reconsider the definition without trying so hard to make it fit your preconceived notions based on non-mathematical language.
Apr
28
answered What is an Empty set?