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Apr
13
comment Can abstract algebra be used to prove points are constructible?
@user54301 That's exactly what I said in my answer.
Apr
13
comment Intersection of two circular arcs with same center
@tjvg1991 Do you know the start points and end points? If so, what format are those points in? That is, do you know their coordinates, or their angular positions, or what? Obviously if you don't know the start and end points, the problem is impossible.
Apr
13
revised Intersection of two circular arcs with same center
edited tags; edited title
Apr
12
comment How to find a definite integral over a symmetric interval without finding the antiderivative?
Why would the integral not exist? It's a continuous function on a closed, bounded interval.
Apr
11
answered Proving an equivalent statement for the Stone-Weierstrass theorem
Apr
10
answered Can abstract algebra be used to prove points are constructible?
Apr
10
asked A comment in the Disquisitiones Arithmeticae
Apr
8
comment Generator of group, find the inverse, solve equation
Of course we can find the exact number - $p$ is explicitly given, so in principle you could just try every number between $1$ and $p$ and check if it's a generator, thus counting the number of generators.
Apr
8
comment A pedagogical proof that 9's can be ignored when calculating digital roots
One approach would simply be to namedrop "modular arithmetic" and say that it involves advanced math. This would hopefully have the effect of giving the students a sense of wonder and building their interest in mathematics.
Apr
5
comment Has lack of mathematical rigour killed anybody before?
In fact, statistics in general is probably a good place to look for examples of this sort of thing.
Apr
5
comment is “$a^0 = 1$” a definition or there exists a proof?
In a way, it's obvious that it's a definition. If $a^n=aaa...a$, $n$ times, then $a^0$ just flat out doesn't make sense, so it clearly needs to be given a special meaning before it can be said to have any value at all.
Apr
5
comment is “$a^0 = 1$” a definition or there exists a proof?
@EnjoysMath Are you being serious?
Apr
5
comment What does the notation $\mathbb R[x]$ mean?
$\mathbb R[x]$ couldn't possible mean $\mathbb R^n$. The notation $\mathbb R^n$ includes a variable $n$ which appears nowhere in the notation $\mathbb R[x]$.
Apr
4
revised Why exponent of exponent multiplied?
edited tags
Apr
3
comment Why only the numerator is derived?
To whom it may concern: please don't downvote questions because you think they're elementary.
Apr
3
reviewed Reject Why only the numerator is derived?
Apr
3
answered Is every integer a unary operation?
Apr
3
comment Finding the curvature of a line.
Not every curve can be aligned with a circle. Unless what you're really asking is "given the width/height of a circular arc, how can I determine how big the circle it's from is?".
Apr
2
comment Why is the construction of the real numbers important?
@industry7 That would certainly be another approach to motivating the concept of a real number. I chose my "if you needed a square root of two, you'd just pick an approximation" story because it's purely arithmetical (even if I chose to illustrate it with geometry). We just seem to be using the word "obvious" in different ways.
Apr
2
comment Why is the construction of the real numbers important?
@AsafKaragila If rationals are just equivalence classes, how do you justify their relation to the real world? How do you justify that chopping something into three pieces gives $1/3$ of what you originally have? Also, you then have to simply define the operations somewhat arbitrarily, when deep down you secretly know that those operations can be proven (informally, but still convincingly) to be correct. This dissonance between the formalization and your intuition means that the formalization isn't really useful, and rationals are pretty much just fundamental objects.