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May
2
answered What does it mean for two matrices to be orthogonal?
May
2
answered why are equivalence relations called so?
May
2
answered $\text{Alt}\,(\phi_1 \otimes \phi_2 \otimes \phi_3)$
May
2
revised Why is a “reverse surjection” incorrect?
expanded a bit about the differences when using functions and general relations
May
2
answered Why is a “reverse surjection” incorrect?
May
2
reviewed Approve examples of a special problem in linear transformation
May
2
answered examples of a special problem in linear transformation
May
2
comment examples of a special problem in linear transformation
How do you define "distinct"? Does $T=2S$ already count as distinct?
May
2
comment Determinant of a otherwise constant matrix with a constant diagonal
Subtract the second row from the first.
May
2
comment How to prove that $\frac{a}{b}$ is irrational when knowing that $a$ and $b$ are irrational and $a$ and $b$ are co-primes
Anyway, even if you could prove the claim, that would not solve your given task because you'd not use the change of base rule.
May
2
answered Prove that left and right inverses are equal
May
2
comment $K$ is convex.Is this true that ${K^ \circ } \ne \emptyset$?
What is the smallest convex set you can think of? What it its interior?
May
2
answered Can mathematical inductions work for other sets?
May
2
comment Can mathematical inductions work for other sets?
There is a recent blog post about this topic.
May
2
comment Ho many nonnegative integer solutions does the equation $2x_1 + 2x_2 + x_3 + x_4 = 12$ have?
What have you tried yet?
May
2
comment Ho many nonnegative integer solutions does the equation $2x_1 + 2x_2 + x_3 + x_4 = 12$ have?
Are solutions which are permutations of each other (say $(3,3,5,1)$ vs. $(3,3,1,5)$) to be counted separately?
May
1
answered What is a basis for the vector space $ \Bbb{C}^{n} $ (a complex vector space)?
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?