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Jun
21
comment Motivation Behind Tschirnhaus Transformation and Cardano's Formula
@Damien What do you mean by the "motivation" for the change of variable $t = y - a/3$? Do you mean (1) why do we want to eliminate the quadratic term, or (2) how do we know that that substitution will do that?
Jun
21
revised An unsolvable Number Theory Question
deleted 67 characters in body
Jun
20
accepted Where am I going wrong in this Gram-Schmidt calculation?
Jun
20
comment Where am I going wrong in this Gram-Schmidt calculation?
Once to normalize $a_1$, and once again to cancel out the factor of $||a_1||$ from the scalar product?
Jun
20
answered Is this polynomial irreducible in $\mathbb{Q}$?
Jun
20
revised Where am I going wrong in this Gram-Schmidt calculation?
added 12 characters in body
Jun
20
asked Where am I going wrong in this Gram-Schmidt calculation?
Jun
20
comment $\infty + \infty = \infty$?
Excuse me, but $\infty + \infty = \pi$. At least under my notation. But how are you defining the symbol $\infty$?
Jun
20
reviewed Approve suggested edit on Derivative of rational function help.
Jun
20
comment Completion of a metric space vs. field extension
For point (2), note that $\mathbb R$ is not an algebraic extension of $\mathbb Q$.
Jun
20
comment Completion of a metric space vs. field extension
Of course not, because the metric need not have anything to do with the field. As far as the metric is concerned, $F$ is just a set. Things might get interesting if the field operations are required to be continuous for the metric.
Jun
20
comment Recursive Set Challenge
What do $\leq_m$ and $\leq_1$ mean?
Jun
20
comment Interesting Number Game
This is just one example of a class of game that you see a lot, but which as far as I know isn't very well studied. Describing the span of a set under some operations tends to be quite easy, however, adding restrictions on how many times those operations can be done seems make the problem very difficult.
Jun
20
revised Interesting Number Game
edited tags
Jun
19
comment Category-theoretic description of the real numbers
Your question body seems to be at odds with the title. The title seems to be asking for practical or philosophical reasons why we should study the real numbers, but the question body seems to be asking "How do the real numbers fit into category theory?". In particular, I think when you say "from a mathematician's point of view" you mean "from a category theorist's point of view".
Jun
19
revised Validity of a trigonometric proof that $2 = 0$.
edited tags
Jun
19
comment Validity of a trigonometric proof that $2 = 0$.
What's going on with these downvotes? This is a legitimate non-duplicate question asking where the fallacy is in a particular argument.
Jun
18
revised Questions on limit superiors
edited title
Jun
18
comment Proof of the derivative of $a^x$
@user157789 Some people would take it as the definition of $a^x$.
Jun
17
revised Why do the negative-exponent terms vanish in this proof of the Residue theorem?
edited body