Definitions for up to
This page provides all possible meanings and translations of the word up to
busy or occupied with
"what have you been up to?"; "up to no good"
adequate to(p), capable, equal to(p), up to(p)(adj)
having the requisite qualities for
"equal to the task"; "the work isn't up to the standard I require"
Against; next to; near; towards; as far as.
As much as; no more than.
For the option or decision of.
Doing; involved in (with implications of mischief).
Incumbent upon; the obligation of; the duty of.
Considering all members of an equivalence class the same.
In mathematics, the phrase up to indicates that its grammatical object is some equivalence class, to be regarded as a single entity, or disregarded as a single entity. If this object is a class of transformations, it implies the equivalence of objects one of which is the image of the other under such a transformation. If X is some property or process, the phrase "up to X" means "disregarding a possible difference in X". For instance we might follow the statement "an integer's prime factorization is unique up to ordering", meaning that the prime factorization is unique if we disregard the order of the factors; or we might say "the solution to an indefinite integral is f(x), up to addition by a constant", meaning that the added constant is not the focus here, the solution f(x) is, and that the addition of a constant is to be regarded as a background, of secondary focus. Further examples concerning up to isomorphism, up to permutations and up to rotations are described below. In informal contexts, mathematicians often use the word modulo for similar purposes, as in "modulo isomorphism".
Translations for up to
Kernerman English Multilingual Dictionary
as far, or as much, as
He counted up to 100; Up to now, the work has been easy.
- tot byAfrikaans
- atéPortuguese (BR)
- až doCzech
- op til; indtilDanish
- έως, μέχριGreek
- -ig (pl. százig, mostanáig)Hungarian
- upp að; fram aðIcelandic
- fino aItalian
- tot ... toeDutch
- (inn)til; opp til, så langtNorwegian
- (aż) doPolish
- până laRomanian
- до (сих пор)Russian
- až doSlovak
- [upp] till, fram till, hittillsSwedish
- ...-e/a kadarTurkish
- 直到...Chinese (Trad.)
- lên tớiVietnamese
- 直到...Chinese (Simp.)
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