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Jul
30
comment Continuity Must Hold in an Entire Open Set?
@Mehrdad: I believe $g(x) = x^2$ for $x \in \mathbb Q$, $g(x) = -x^2$ otherwise, should qualify.
Jul
30
comment Continuity Must Hold in an Entire Open Set?
Your question title is still asking the opposite question as your last paragraph.
Jul
28
comment Must all Lebesgue integrable functions really be invertible?
@Kyle: If only one other user besides the author has commented on a post, they will be automatically notified when the author posts a comment, even if there's no @user tag. So your making sure, though surely well meant, was actually unnecessary in this case.
Jul
28
revised Must all Lebesgue integrable functions really be invertible?
misc. copyedits, improve(?) tags
Jul
28
revised Must all Lebesgue integrable functions really be invertible?
fix missing $
Jul
28
revised Must all Lebesgue integrable functions really be invertible?
fix misplaced braces
Jul
17
answered Do the matrices with maximum determinant always have integral values
Jul
16
revised Find the order of an element of finite group
fix typo
Jul
16
comment Guessing the probability by results of just 1 experiment
Related: math.stackexchange.com/questions/130254/…
Jul
16
comment Coin with unknown bias flipped N times with N heads, what is p(h)?
@MJD: That's because most coins you've flipped have probably been more or less fair, so your experience has a strong prior bias towards $p \approx \frac12$. Thus, the implicit flat prior assumed by the Rule of Succession doesn't really match your experience well.
Jul
12
answered Unable to understand the proof of two isomorphic finite-dimensional vector spaces having the same dimension
Jun
17
comment What is a negative number?
... You could just as well develop the unsigned reals before adding negative and complex numbers into the mix, as in the book you mention; or, if you really wanted, even develop the Gaussian integers and Gaussian rationals before introducing real numbers in any form.
Jun
17
comment What is a negative number?
+1 for noting that the positive reals can be easily and naturally defined without making any use of negative numbers. In fact, I'd say that there are really two orthogonal axes in the (historical / formal) development of the number system: one goes unsignedsignedcomplex and the other goes integerrationalreal. In developing the number system, you can traverse these axes in any order; while the usual way involves taking one step from the naturals to the signed, then traversing the other axis to the signed reals, and finally complexifying them, that's not the only path.
Jun
17
comment What is a negative number?
I agree with @Jared that the actual question in this question is unclear, and I'd even say that the suitability of this question to Stack Exchange is at best marginal. To quote our help center, "You should only ask practical, answerable questions based on actual problems that you face." I haven't actually voted to close this question, since it is getting interesting answers and the comments seem to be staying under control, but I may change my mind if this ends up degenerating into an infinite diverging sequence of "But what is is?" comments.
May
19
revised Short exact sequence - Why doesn't this argument work?
tidy up mathjax
May
14
comment Proving a trigonometric identity: $\frac{\cos x}{1-\sin x} -\tan x = \sec x$
@User58220: Why on earth not? The only issue to watch out for with cross-multiplication is that it can introduce extraneous solutions where either (or both) of the denominators is zero. But that has nothing specifically to do with trig.
May
10
comment In how many ways can a $5 \times 5$ matrix be formed such that sum of row elements and column elements are $4$ and entries are $0$ or $1$?
No, explaining how you got the number 120 is the answer. ;-) But yes, the number of 5 × 5 matrices satisfying these conditions is 5 × 4 × 3 × 2 × 1 = 5! = 120.
May
10
comment In how many ways can a $5 \times 5$ matrix be formed such that sum of row elements and column elements are $4$ and entries are $0$ or $1$?
OK, I edited in some more explicit hints.
May
10
revised In how many ways can a $5 \times 5$ matrix be formed such that sum of row elements and column elements are $4$ and entries are $0$ or $1$?
added 503 characters in body
May
10
answered In how many ways can a $5 \times 5$ matrix be formed such that sum of row elements and column elements are $4$ and entries are $0$ or $1$?