## How to compare number from newenvironment argument

I am trying to create a new environment as follows

``````newenvironment{letters}[1]{%
vspace{-3mm}
ifnum #1=1%
else
begin{multicols}{#1}
fi
begin{enumerate}[label=textbf{(alph*)}]
}{%
end{enumerate}
ifnum #1=1%
else
end{multicols}
fi
vspace{-5mm}
}
``````

My question is: Why doesn’t it work?!

Note: this is not a duplicate from this post, since I don’t want to do the `RenewDocumentEnvironment`. Instead, I want to create a new environment.

## Number fields ordered by discriminant

Since the discriminant of a number field $$K neq mathbb{Q}$$ is bounded from below by an exponential of the degree $$[K:mathbb{Q}]$$, for instance by Minkowski’s Geometry of Numbers bound, there are finitely many number fields $$K$$ below a given discriminant bound $$|D_{K/mathbb{Q}}| leq X$$. Let $$mathcal{S}(X)$$ be that finite set.

Question. What is a good guess for the order of growth of $$# mathcal{S}(X)$$ as a function of $$X$$? Any reasons to expect (or to doubt) that this count should be asymptotic to a regular (say, smooth) function of $$X$$?

If so, what about finer statistics of number fields at large (unconstrained degrees with $$|D_{K/mathbb{Q}}|$$ as the sole parameter), such as the function of typical degree $$d(X) := frac{1}{#mathcal{S}(X)} sum_{K in mathcal{S}(X)} [K:mathbb{Q}]$$, the mean Euler-Kronecker invariant $$gamma_K$$, or the mean minimum height of a generator of a random number field,
$$h := lim_{X to infty} frac{1}{#mathcal{S}(X)}sum_{K in mathcal{S}(X)} min_{alpha: , K = mathbb{Q}(alpha)} h(alpha) in [0,infty].$$
Assuming this extended number $$h$$ exists, should it be $$0$$, $$infty$$, or a positive finite number? The former alternative would mean that when number fields are ordered by discriminant, a random number field can be generated by a root of an integer polynomial whose coefficients are asymptotically sub-exponential in the degree. The second alternative would mean that a random field requires more than an exponentially large coefficients for all of its generating elements. While the third alternative says that a random number field has the Bogomolov height gap property.

## Discrete: possible number of ways of arranging odd numbers in odd position.

How many 7-digit naturals can be formed by catenating all of 1, 2, 2, 3, 3, 3, 4 if the odd naturals in this list must always occupy the odd positions?
the order be like for example 1, _, 3, _, 3, _, 3 where the odd numbers are in the odd positions. I know we have to use combinations. Is it correct?

## What is the maximum number of characters in a currency symbol?

In the program I am writing, I need to show a currency selector. I would like it to display currency symbols. For this, I need to know what is the longest, in characters, currency symbol (or rather what the maximum length can be, if there is any limitation).

E.g. USD, EUR, RUB all use single-character symbols: \$, â¬, â½. I initially assumed that it will always be one character. But I am obviously wrong, as e.g. Polish zloty symbol is zÅ.

## Phone number column validation

I want to add phone number column with below format:

`1-121-343-6917`, `434-5503` & `60-12-444 444`

Used below method

```=TEXT(123456 ,CHOOSE( LEN(123456) ,"0" ,"00" ,"000" ,"0-000" ,"00-000" ,"000-000" ,"0-000-000" ,"00-000-000" ,"000-000-000" ,"0-000-000-000"))```

But this troublesome when you input information in EDIT mode rather than add NEW ITEM.

How I can use validation? Need help urgently.

## ArgMax giving error “The function value *** is not a number at **”, but the exact same expression works in…

I am trying to ArgMax the following function:

``````ArgMax[{0.5 ln[2 (1 - [Alpha])] + 0.5 ln[4. [Alpha]]}, [Alpha]]
``````

This expression works flawlessly in WolframAlpha (link), but it doesn’t work in Mathematica Desktop 11.3.0.0.

It seems like that Mathematica is trying to evaluate alpha in a domain that alpha is not suppose to be, so I also tried assuming.

Any thoughts?

## Should I provide my insurance policy number after returning a rental car without any damage (USA)?

A car rental company charged me with a security deposit when I was renting the car. I returned the car in original condition and with extra gas in the tank. They have not returned my security deposit yet. Today, they called me and asked me to give them my car insurance policy number to return the security deposit. Should I give them that policy number? I do not trust them, is this normal?