962 reputation
21528
bio website
location
age
visits member for 4 years
seen Sep 30 at 3:10

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?
Mar
30
awarded  Cleanup
Mar
30
revised Why does $a_n = (1+\frac{2}{n})^{n}$ converge to $e^2$?
rolled back to a previous revision
Mar
29
accepted Why does $a_n = (1+\frac{2}{n})^{n}$ converge to $e^2$?
Mar
29
comment Why does $a_n = (1+\frac{2}{n})^{n}$ converge to $e^2$?
Thank you very much for this answer. Just one question: why is the first limit going to zero rather than infinity?
Mar
29
asked Why does $a_n = (1+\frac{2}{n})^{n}$ converge to $e^2$?
Mar
13
accepted Proving elementary inverse image consequence
Mar
13
asked Proving elementary inverse image consequence
Mar
11
comment Is a linear tranformation onto or one-to-one?
oh ok, so it wouldn't have been a function in the first place... Thanks for clearing that up for me! And thanks for another great answer of course!
Mar
11
comment Is a linear tranformation onto or one-to-one?
Sorry if this is a stupid question, but is it always the case that whether a function is one-to-one depends only on the domain? For instance with the example $f(x) = x^2$ if the codomain were $0$, wouldn't the function still be one-to-one?
Mar
7
comment Proving $(2n+1) + (2n+3) + \cdots + (4n-1) = 3n^{2}$ for all positive integers $n$
Thank you for the answer, although I must say that it isn't the same without the bold HINT formatting ;)
Mar
7
comment Proving $(2n+1) + (2n+3) + \cdots + (4n-1) = 3n^{2}$ for all positive integers $n$
Definitely helps a lot, thank you!
Mar
7
accepted Proving $(2n+1) + (2n+3) + \cdots + (4n-1) = 3n^{2}$ for all positive integers $n$
Mar
7
comment Proving $(2n+1) + (2n+3) + \cdots + (4n-1) = 3n^{2}$ for all positive integers $n$
thank you for the reply, I can understand much more now. Just to be absolutely clear: in order to determine which terms are added/deleted one could replace each $n$ in the original LHS with $n+1$, correct?
Mar
7
comment Proving $(2n+1) + (2n+3) + \cdots + (4n-1) = 3n^{2}$ for all positive integers $n$
Unfortunately I still don't get it... with the induction, is it correct to sort of 'plug in' $n+1$ for each $n$? And somewhere in between $(2n+5)$ and $(4n-1)$ each term begins to be calculated differently? I can see why $2n+1$ is some odd number, but what is $4n-1$?
Mar
7
asked Proving $(2n+1) + (2n+3) + \cdots + (4n-1) = 3n^{2}$ for all positive integers $n$
Feb
28
awarded  Civic Duty
Feb
27
awarded  Suffrage
Feb
13
comment Why is the 'change-of-basis matrix' called such?
@Qiaochu, is 'in the basis given by' the same as 'relative to the basis'?