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May
1
comment Is this writing incorrect?
I would at least make parentheses around the $x^2$ in the derivative (that is, $\frac{d}{d(x^2)}$), to make clear that it's not the derivative operator itself that's squared (as it would be for the second derivative, $\frac{d^2}{dx^2}$).
May
1
comment If there are injective homomorphisms between two groups in both directions, are they isomorphic?
@AsafKaragila: Thank you for the explanation. So essentially what you're saying is that Qiaochu's counterexample doesn't work that way for ordered fields because those are not completely determined by their cardinality. Unfortunately that still doesn't tell me the answer of the original question for ordered fields.
May
1
comment If there are injective homomorphisms between two groups in both directions, are they isomorphic?
@AsafKaragila: What does it mean for a theory to be categorical in a cardinality?
May
1
revised A valid method of finding limits in two variables functions?
added 19 characters in body
May
1
revised A valid method of finding limits in two variables functions?
added 19 characters in body
May
1
comment Which mathematical topics should an applied math major know to be employable in industry?
Probability and statistics is certainly a must — even if it is not specifically needed for your job. If nothing else, it will allow you not to fall for the all to common lies "supported" with appropriately presented statistics.
May
1
comment Compute $\lim_\limits{n\to\infty}a_n$ where $a_{n+2}=\sqrt{a_n.a_{n+1}}$
You got the exponent of the limit wrong. But since the derivation is correct and great, +1 anyway.
May
1
answered Compute $\lim_\limits{n\to\infty}a_n$ where $a_{n+2}=\sqrt{a_n.a_{n+1}}$
May
1
answered $5x\equiv3\pmod3$
Apr
30
comment If there are injective homomorphisms between two groups in both directions, are they isomorphic?
What about ordered fields?
Apr
30
comment Confused with imaginary numbers
Of course $-1=1$ because $-1 = \sqrt{-1}^2 = \sqrt{(-1)^2} = \sqrt{1} = 1$. Thus $-\mathrm i = -1\mathrm i = 1\mathrm i = \mathrm i$. :-)
Apr
30
comment What does $(m, n) = 1$ mean?
I actually think the parenthesis notation is overloaded too much. $(a,b)$ may be a pair, an interval, a gcd … anything else?
Apr
30
answered Zeroes of sin(x)
Apr
30
accepted What questions are independent from the axiom of constructibility?
Apr
28
answered Point in four dimensions
Apr
28
answered True or false: sets, subsets, and topologies in $\mathbb R$
Apr
28
revised Tangent of Circles
A meaningful alt tag for the image
Apr
28
comment What questions are independent from the axiom of constructibility?
What does Con(ZFC) mean?
Apr
28
asked What questions are independent from the axiom of constructibility?
Apr
26
awarded  Sportsmanship