mm k im supposed to just look at the degrees of the exponentials i guess

makes sense

lol

nvm im still confused

$$\frac{Nk_B(\varepsilon\beta)^2 \exp(\beta\varepsilon)}{(\exp(\beta\varepsilon)-1)^2}\approx Nk_B(\beta\varepsilon)^2\exp(-\beta\varepsilon)$$ since $\beta\varepsilon\to\infty$ as $T\to 0$ idk how this follows

Do you want it the math way or the physics way?

Either way :P

I'll let others speak to it the math way. For the physics way you simply observe that $(\exp(\beta\varepsilon)-1)^2 \to (\exp(\beta\varepsilon))^2$ in this large $\beta$ limit. Then cancel one factor of $\exp(\beta\varepsilon)$ from the top and bottom.

ohh okay

what about the other way when $\beta$ gets to be close to 0

somehow it approximates to be $3Nk_B$

Expand $e^x \approx 1+ x$ and see what happens :)

OHH right

u can do that

bless u :P

Cheers

A "soft" question about math writing for folks here: how do you deal with nested brackets? For example, suppose I wanted to write an aside in brackets, and in that aside I refer to some equation, say equation (2.65). Would you choose square brackets in this case or is that bad form?

(This follows from equation (2.65)) or [This follows from equation (2.65)]

I think the former is perfectly fine, but when Xander arrives, he will probably be able to point you to the precise subsubsection in the AMS style guide where this is addressed

or you could say (this follows from equation 2.65)

Certainly I am not writing anything so important as to deserve that :) but thanks Thorgott

That's fair Obliv, but generally the brackets are there in the label too which is why i have them

@Thorgott There isn't actually a ton there, though the inference I draw is that "This follows from (2.65))" is the preferred style (note that is just "(2.65)", not "equation (2.65)").

E.g. section 6.4

> Identifying letters ((a), (b), (c)), including their parentheses, are roman in all text. The AMS will allow italic identifying letters only if consistent throughout.

Section 13.14:

> In cross-references, equation numbers are enclosed in roman parentheses to match the original label and the parentheses are always roman.

(which only says that equation numbers should always be in parentheses, not other kinds of braces).

On the other hand, the only references that the style guide has to brackets is in the context of citations and "fences" in mathematical contexts. I do not think that AMS editors would be too happy with square braces for parenthetical content.

Personally, I would seek to rewrite the phrase.

@Obliv No. This is wrong. Again, see section 13.14 of the AMS style guide.

For the reference of others: ams.org/publications/authors/AMS-StyleGuide-online.pdf

i don't think style can be logically deduced

@Obliv Okay...