An additional classical usage of Zorn's lemma is definitely the proof that each correct suitable—that may be, an ideal that's not The entire ring—of a ring is contained in a maximal best. Here, S displaystyle S
as well as list of all true numbers hold the identical cardinality, a bijection being supplied by the operate x ↦ tan ( π x / 2 ) displaystyle xmapsto tan(pi x/2)
The decide has set the date with the trial. Established also has some standard intransitive makes use of, as “to go beneath the horizon” ( The Solar sets late during the northern latitudes in the summertime
The remainder, unable to provide any more, or prepared to fall to thrift, must be placed partially from the lands by them won, at greater amount than Other individuals, to whom the same shall be set out.
We may still doubt whether the Lord, in these indifferent ceremonies as People whereof we dispute, did frame his folks of established purpose unto any utter dissimilitude with Egyptians, or with dich vu do cung any other country.
or S is often a established and S ∉ S displaystyle shade crimson S text is really a established and Snot in S
Now we have inventory ample to arrange with, capable of infinite development, and however no fewer able to whole decay.
Specifically, a line wasn't considered as the list of its factors, but to be a locus exactly where factors may very well be located.
Intuitively, an indexed relatives is really a established whose things are labelled with the elements of another established, the index established. These labels allow the similar component to happen quite a few moments within the family.
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[ T constantly + adv/prep ] existing participle location
set 1's house to be able : to organize 1's affairs established a single's sights on : to ascertain to pursue set a single's enamel on edge : irritate, annoy set one straight : dich vu do cung to accurate another person by giving precise data established sail : to begin out on the system Particularly : to begin a voyage
Some logical formulas, such as S is often a set displaystyle shade pink S text can be a established
b of a dye dich vu do cung or shade : to be long term c of the bone : to become total by growing collectively