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visits member for 3 years, 11 months
seen Sep 30 at 3:10

Apr
17
asked How to show certain things related to scalar products
Apr
17
comment Subtraction and division with integers modulo 3
@Gerry: thanks for the explanation. I had copied that notation from Paul R. Halmos -Linear Algebra Problem Book... But, yeah I will definitely try to avoid using those sorts of fractions in the future.
Apr
17
accepted How do you show this property of a differentiable function given information about the derivative?
Apr
17
comment Subtraction and division with integers modulo 3
Thank you for this answer
Apr
17
comment Subtraction and division with integers modulo 3
@Fabian: thanks for the helpful tips
Apr
17
accepted Subtraction and division with integers modulo 3
Apr
17
comment Subtraction and division with integers modulo 3
@quanta: I'm sorry if I'm just completely missing something here, but are you saying there is a problem with the way I am trying to write down/express an idea, or with the idea itself that I am trying to carry out division on the integers modulo 5?
Apr
17
comment Subtraction and division with integers modulo 3
@quanta: ok, yeah I meant by that 3 divided by 4 in integers modulo 5 (and I realize the way I used $x$ in my above comment was nonsense). But isn't that how you would carry out division of 3 by 4 in integers modulo 5? Since $4$ is the inverse of $4$, $3*4^{-1}=2$ in integers modulo 5, no?
Apr
17
comment Subtraction and division with integers modulo 3
@quanta: thank you for the answer. I'm still digesting it, but I wanted to check if I am understanding part of the idea. If I wanted to divide on say integers modulo 5 (where there are a couple more examples) then for say $\frac{3}{4}=x$ I would first always calculate $4^{-1}$ and then multiply? And because of the gcd stuff you showed, I know that $1\equiv 4x \mod 5 \Rightarrow x = 4 \Rightarrow \frac{3}{4} = 2$? So in these cases it is about finding the inverses first?
Apr
17
asked Subtraction and division with integers modulo 3
Apr
16
comment How do you show this property of a differentiable function given information about the derivative?
@Qiaochu: thanks for that comment, I guess the derivative of a polynomial satisfies $f'(-x)=-f'(x) \Rightarrow f'$ is odd with degree $n \Rightarrow \int f'(x)dx$ is even with degree $n+1$..? Unfortunately I can't say much about a power series or a differentiable function in general...
Apr
16
comment How do you show this property of a differentiable function given information about the derivative?
$g(0) = f(0)-f(-0)=0$ ?
Apr
16
comment How do you show this property of a differentiable function given information about the derivative?
thank you for this answer. Unfortunately I can't manage to finish the problem with it yet. $g(x) = f(x)-f(-x) \Rightarrow g'(x)=f'(x)+f'(-x) \Rightarrow g'(x) =0 \Rightarrow g(x)=C \Rightarrow ?$ is the rest pretty much as Chris shows, or did you have something else in mind? (The only thing is that I don't know how I would have defined all these other functions and so on...)
Apr
16
comment How do you show this property of a differentiable function given information about the derivative?
@Fabian: yeah, careless mistake on my part, thank you for clearing that up
Apr
16
comment How do you show this property of a differentiable function given information about the derivative?
@Fabian: Thank you, I noticed that as well, but wasn't sure if it would turn out to be a 'trick.' As for deducing something: what more than $f(-x) = -f(x)$ or maybe even $f(-x)+f(x)=0$ should I see? Also, why is it ok to evaluate the definite integral here? (sorry if i'm missing very obvious stuff!)
Apr
16
comment How do you show this property of a differentiable function given information about the derivative?
@Thomas: It's not homework, but thanks for the hint anyway. If I integrate both sides of the above equation I get $f(-x) + C = -\int f(x)dx$ right? I am not sure what to do with that and in I general get thrown off by the constant whenever I try to use integration...
Apr
16
revised How do you show this property of a differentiable function given information about the derivative?
edited title
Apr
16
asked How do you show this property of a differentiable function given information about the derivative?
Apr
10
accepted What is the best way to show that no positive powers of this matrix will be the identity matrix?
Apr
10
asked What is the best way to show that no positive powers of this matrix will be the identity matrix?