Translation in english of "section commençante"

[Th.V]

Hello,

(1) In a totally ordered set E, A:={y belongs to E | yla section commençante ouverte" defined by x.
(2) In a totally ordered set E, A:={y belongs to E | y< or equal to x} is "la section commençante fermée" defined by x.

The question is: Is it possible to translate the sentence "la section commençante ouverte" by means of "Initial segment"?


The question is: Is it possible to translate the sentence "la section commençante fermée" by means of "closed Initial segment"?

OR, is there another translation?
Thank you so much in advance for your help.
Kind regards. Th.V

[AuSmith]

This is not exactly UIL mathematics, but it looks good to me, as in I'd say this is the only translation, considering my total authority on translations such as this.

[Th.V]

Thank you so much

[MistaPotta]

Actually I'd lean more towards "open interval" and "closed interval" respectively, but I might be wrong.

[MichaelGummelt]

Ya, open and closed intervals were the first thing that I though of too. We would denote those as:


[unparseable or potentially dangerous latex formula] for the open interval and [unparseable or potentially dangerous latex formula] for the closed interval

[Th.V]

I agree with you,

but A is a subset of the set E, and we have to mention that this is the "beginning" part of E (and not the "ending" part). Ordinals and Ordering are underlying. See

(1) In a totally ordered set E, A:={y belongs to E | y(2) In a totally ordered set E, A:={y belongs to E | y< or equal to x} is "----- ----" (of E) defined by x.

So, what do you think about? Thank you in advance. Th.

[AuSmith]

I'd think either way. Open would further clarify, but is unnecessary.

[Th.V]

Okay I agree. Thanks. Th.