Within your For loop, you're assigning to s, but in your Append your appending s0. Is that the problem, or was s0 just a copy-paste error?

In the meantime, understand that For doesn't produce any output (well, it produces Null actually, but Null doesn't display in the UI by itself). So, if you fix the s versus s0 problem, then your code actually does work. To see the result, just evaluate v1. For me I get:

v1
(* {{15}, {20}, {25}, {30}, {35}, {40}, {45}, {50}, {55}, {60}} *)

Also, you can do this with Table rather than For, which is a bit more natural for Mathematica:

Table[SolveValues[f[x, y] == 0, x, Reals], {y, 1, 10}]
(* {{15}, {20}, {25}, {30}, {35}, {40}, {45}, {50}, {55}, {60}} *)

Notice that Table actually produces an expression as output.

In the first iteration, we'll evaluate an expression like this:

s = SolveValues[-15 + x == 0, x, Reals]

If you evaluate just that expression, it gives:

{15}

So, yes, s was set to be a list of values. There happens to be just one solution, so the length of the list is 1. Everything is working exactly as you describe.

I honestly don't understand your question. Everything is working as expected, and everything is working as you describe. So, what's the problem exactly?

I believe that there are three types of computation results (real numbers, identities and rules). Despite that, Wolfram commands operate a generic function over lists of real number. It sounds natural to you, but for me it is still something interesting (and new as a beginner).

Changing the subject, but it is still related with what you said above that For loops give Null as a result of computation. Well. I have the example of a function that when we apply the SolveValues command to it, we get a list like:

{{e1,e2},{e3,e4},{e5,e6}, ...,{},{},...{}} where e1<e2, e3<e4, etc

Do you know how to sort out lists {e1,e2} and empty list {}?

I did something like this:

hmax=Table[Max[SolveValues[F[x,y]==0,x,Reals]],{y,y0,yf,deltay}]
hmin=Table[Min[SolveValues[F[x,y]==0,x,Reals]],{y,y0,yf,deltay}]

But now hmax has negative infinite symbols and hmin has positive infinite symbol. These lists will mess up ListPlot. The function F[x,y] is something like that:

F[x_,y_]:=x/1.255-(1.127+1.127*y/x+0.1885/x)^(-1)+0.11

By the way, y0=0.0001; yf=0.5 and deltay=0.0005 Can you help me with this problem, please? Thank you very much.

Hi, everyone! Honestly, I have learned right now how to use this dialog box. Thank you, Eric Rimbey! Well, my problem is about using the FOR loop in the following case:

f[x_,y_]:= x - 5*y - 10;
v1={};
For[y=1,y<=10,y++,s=SolveValues[f[x,y]==0,x,Reals];AppendTo[v1,s0]]

There is something wrong with this code, because s has not been evaluated at each iteration.
If there is a better way to solve with Wolfram functions, I would love to know about that.
Please, help me out in dealing with this issue. Thank you in advance for your help.