>>914
Oh, I see now. 

As you've checked what I described for taking L the positive integers, you've checked things in accordance with induction as I state in >>882. 

The difference between all of the positive integers and infinity is for example their names: "All of the positive integers" is not the same string of symbols as "infinity", one is to justify their equality if one is to claim it. Indeed a further difference is that the former is meant to be a set and the latter is not. This shows their inequality and one cannot show their equality hence.

The reason it's a one liner is as it's straightforward. 
You're asking for something similiar as to asking to justify that the natural number 2 and infinity are different. They are different as can be seen by looking at them. Another example is asking why water is different from air, it just is.