I do not have a background in mathematics. However, I do empirical research and I oftentimes have difficulties finding the correct mathematical notations for certain things I want to express:

I am comparing two sets of values. Each value in one set relates to a certain value in the other set, i.e. the two sets represent a set of "pairs". How do I express that, e.g. more than half of the values in one set are larger than their respective counterpart in the other set?


Let the two sets be $A$ and $B$; the wording implies that they are finite. You say that all the elements can be paired, so there is a bijective function $f:A\mapsto B$ expressing this relation. Call the cardinality of each set $n$.

Your last sentence may then be written as $$|\{a\in A:a>f(a)\}|>\frac n2$$

  • $\begingroup$ Does a similar notation hold for vectors? For example, if A and B are vectors, does the notation still hold? $\endgroup$ – shenflow Apr 20 '20 at 10:00
  • $\begingroup$ @shenflow I suppose so, if you regarded vectors as ordered multisets. $\endgroup$ – Parcly Taxel Apr 20 '20 at 10:04
  • $\begingroup$ Alright. So using a different notation for vectors, one could say $f: \vec{A} \mapsto \vec{B}$, etc.....? Thank you in advance. $\endgroup$ – shenflow Apr 20 '20 at 10:12
  • $\begingroup$ @shenflow I would put $f:\mathbb R^n\to\mathbb R^n$ or something similar. $\endgroup$ – Parcly Taxel Apr 20 '20 at 10:13
  • $\begingroup$ Okay. So you would put that. Then say that the two vectors are elements of the domain and codomain respectively. And then say $$|\{a\in A:a>f(a)\}|>\frac n2$$ to express that more than half of the elements in A are larger than their counterpart in B? Sorry if this gets to extensive, maybe I should post this as a question on its own. $\endgroup$ – shenflow Apr 20 '20 at 10:18

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.