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Oct
30
revised do the uniformly continuous functions to the reals determine the uniformity?
added 536 characters in body
Oct
29
comment if $A^2 = A$ then $|A|=0$ or $|A| =1$
how is it an intuitive jump, knowing that $\alpha = \beta$ and concluding that $f(\alpha)=f(\beta)$? What in that step seems to you to be a bit shaky?
Oct
29
revised do the uniformly continuous functions to the reals determine the uniformity?
edited tags
Oct
29
asked do the uniformly continuous functions to the reals determine the uniformity?
Oct
28
comment Are there contradictions in math?
no @KyleDelaney I do not agree to that at all. Without even getting into the discussion of whether maths is discovered or created (and I don't accept this dichotomy at all), the claim that just because something is created by us, then we have control over it is unfounded. I can state the axioms of set theory, and thus have created set theory, but that does not mean I can make sure it does not have contradictions. Blame Goedel for that one.
Oct
28
answered Is every equivalence of monoidal categories a monoidal equivalence?
Oct
26
answered Is there a power series with $0$ radius of convergence?
Oct
26
answered Exercise 1.2.10 from Model Theory by Chang and Keisler.
Oct
26
answered What does $\mathbb{R}^\mathbb{N}$ actually mean?
Oct
23
answered Show that $d: X \times X \rightarrow \mathbb{R}$ is a metric on $X$
Oct
21
comment How to categorize Measures, Topologies, Algebraic Structures, etc
Please remember that such taxonomies should not be taken too seriously. The divides between the areas is mostly artificial.
Oct
20
comment What is the purpose of showing some numbers exist?
@MvG quite true. I did not say that one should not discuss something before that something is shown to exist. Contemplating whether something exists or not is an important thing to do, and part of that contemplation is discussing what might potentially be the consequences of its existence or non existence. What the properties of such a thing may be. Sure, this is quite alright to do. But before you go ahead and 'use' something, it's wise to make sure it exists. Also, I'm saying this in the context of modern mathematics. The illnesses of pre-axiomatic mathematics are behind us now.
Oct
20
comment Is both $\{\}$ and $\{\{\}\}$ same element $?$
You question has the same answer as the following question: Is an empty bag inside an empty bag the same thing as an empty bag?
Oct
19
comment Looking for Proofs Of Basic Properties Of Real Numbers
I assumed OP was referring to the usual second order axiomatization of the reals where no contradiction is known.
Oct
19
comment mean value theorem differentiability hypothesis violation
What is this image showing exactly?
Oct
19
comment mean value theorem differentiability hypothesis violation
This should have been a comment, not an answer.
Oct
19
comment mean value theorem differentiability hypothesis violation
what on earth would $f'$ be if the function is not differentiable???
Oct
19
comment I don't understand how the theory of algebraically closed fields admits quantifier elimination
Did you try to read the proof that the theory of algebraically closed fields admits quantifier elimination? such a proof will construct, for a given formula, an equivalent quantifier free one. Commonly, once quantifier elimination is established, one proves completeness. This is standard and can be found in many texts.
Oct
18
awarded  Enlightened
Oct
18
awarded  Good Answer