Suppose I am given the numbers from 1 to 9:

1 2 3 4 5 6 7 8 9

I filter out the prime numbers:

2 3 5 7 (A)

and I am left with:

1 4 6 8 9 (B)

What do you call (A) and (B) with respect to the filtering?

I am not sure if "filtered out" refers to the component which was removed, or the component which was retained.


Mathematicians use the term residue for anything left over, which fits nicely with the concept of filtering. I would call (B) the residue and (A) the filtrate in your example. The residue in this case, by the way, is the union of the positive composites and the unit 1.


Oxford Dictionaries

Often also called the remainder, which is listed as a synonym for residue at Oxford dictionaries, but the more usual expression in Mathematics is to call it a residue.

Also, from Mathworld

| improve this answer | |
  • residue is used for anything left over, the examples given at Mathworld are just examples. – JMP Apr 1 '15 at 9:06
  • I'd remembered the word residue from chemistry class, but didn't remember the word from set theory. Thanks for the refresher! – J.R. Apr 1 '15 at 9:53

"Filtered out" would refer A as it was the set that was removed.

(B) I would call the set "that remains" or something similar. There may be a better word for (B)

| improve this answer | |
  • 1
    For (B) you could use "remaining numbers" – user3169 Apr 1 '15 at 6:31

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.