After 13 hr I am still thinking if you mean by cardinality of rational numbers are same from (10^n,10^(n+1)) to (10^(n+1),10^(n+2)). Otherwise I don't know what that means ;_; . I am wishing future me bring same book to me but corrected and clearly explained edition.
My apologie to be unable to grasp what you mean . I am kinda dumb when it comes to understanding what other means I mostly precieve ideas visually so it will take me sometime or may be I will never able to understand it unless provided alternative approach.
@Stupidquestioninc I think you have difficulty with English. I said that there are the same number of rationals of some form in each interval of some form.
Let r(n) be the number of rationals in the interval [10^n,10^(n+1)] that are of the form Sum { d[i]·10^−i : i∈{1..k} } · 10^n where k∈ℕ and n∈ℤ and d[i]∈{0..9} for each i∈{1..k} and d[1]∈{1..9}. Then r(n) is the same for every integer n.
@MEcho If you have a mathematical question, just go ahead and ask it, and provide your thoughts and attempts, and if nobody else answers it I will answer if I can.
Is there a "glossary" of theorems that hold for vector spaces but not modules? As I understand the only difference between them is that modules act on a ring, and vector spaces on a field.
