From: Thorsten Altenkirch <Thorsten....@nottingham.ac.uk> To: Michael Shulman <shu...@sandiego.edu> Cc: "homotopyt...@googlegroups.com" <homotopyt...@googlegroups.com> Subject: Re: [HoTT] "Identifications" ? Date: Mon, 4 May 2020 14:17:23 +0000 [thread overview] Message-ID: <7A5CCED7-4FFC-43EE-AD3C-699899C19520@nottingham.ac.uk> (raw) In-Reply-To: <CAOvivQz1avq5PgK1FHWp1d4-U6UzV=Vdvo9iRp_3WjaXxNUskg@mail.gmail.com> This seems reasonable. I usually say "equality proofs" but the word proof also has other conotations. Also what is an element of 3 <= 4, if not a proof or evidence? Maybe it is a inidentification? __ Thorsten On 04/05/2020, 14:17, "Michael Shulman" <shu...@sandiego.edu> wrote: I don't think using "identification" necessarily implies any difference between "identification" and "equality". I don't think of it that way. For me the point is just to have a word that refers to an *element* of an identity type. Calling it "an equality" can have the wrong connotation because classically, an equality is just a proposition (or a true proposition), whereas an element of an identity type carries information. Calling it "an identification" suggests exactly the information that it carries: a way of identifying two things. On Mon, May 4, 2020 at 2:35 AM Thorsten Altenkirch <Thorsten....@nottingham.ac.uk> wrote: > > I am just reading a paper which uses the word “Identification” instead of equality. I think this has been proposed by Bob Harper. Can anybody enlighten me what is the difference between identifications and equality? Maybe there is an identification between them but they are not equal? Are the real numbers 0.999… identified or are they equal? > > > > Thorsten > > This message and any attachment are intended solely for the addressee > and may contain confidential information. If you have received this > message in error, please contact the sender and delete the email and > attachment. > > Any views or opinions expressed by the author of this email do not > necessarily reflect the views of the University of Nottingham. Email > communications with the University of Nottingham may be monitored > where permitted by law. > > > > -- > You received this message because you are subscribed to the Google Groups "Homotopy Type Theory" group. > To unsubscribe from this group and stop receiving emails from it, send an email to HomotopyT...@googlegroups.com. > To view this discussion on the web visit https://groups.google.com/d/msgid/HomotopyTypeTheory/BBC0B8F3-AB16-4196-B9B9-B1B3031B2D7D%40nottingham.ac.uk. This message and any attachment are intended solely for the addressee and may contain confidential information. If you have received this message in error, please contact the sender and delete the email and attachment. Any views or opinions expressed by the author of this email do not necessarily reflect the views of the University of Nottingham. Email communications with the University of Nottingham may be monitored where permitted by law.
next prev parent reply other threads:[~2020-05-04 14:17 UTC|newest] Thread overview: 26+ messages / expand[flat|nested] mbox.gz Atom feed top 2020-05-04 9:35 Thorsten Altenkirch 2020-05-04 10:59 ` [HoTT] " stre... 2020-05-04 11:04 ` Steve Awodey 2020-05-04 11:17 ` Thorsten Altenkirch 2020-05-04 11:42 ` Nicolai Kraus 2020-05-04 12:04 ` Thorsten Altenkirch 2020-05-04 12:06 ` Thomas Streicher 2020-05-04 12:12 ` Thorsten Altenkirch 2020-05-04 12:39 ` Thomas Streicher 2020-05-04 13:16 ` Michael Shulman 2020-05-04 14:17 ` Thorsten Altenkirch [this message] 2020-05-04 14:48 ` Stefan Monnier 2020-05-04 15:46 ` Nicolai Kraus 2020-05-04 15:57 ` Thorsten Altenkirch 2020-05-04 15:59 ` Michael Shulman 2020-05-04 16:07 ` Steve Awodey 2020-05-04 16:17 ` Thorsten Altenkirch 2020-05-04 16:53 ` Steve Awodey 2020-05-04 17:25 ` Thorsten Altenkirch 2020-05-04 17:43 ` Michael Shulman 2020-05-04 17:55 ` Steve Awodey 2020-05-04 16:21 ` Peter LeFanu Lumsdaine 2020-05-04 16:16 ` Joyal, André 2020-05-04 20:38 ` Joyal, André 2020-05-07 19:43 ` Martín Hötzel Escardó 2020-05-08 10:41 ` [HoTT] " Thorsten Altenkirch
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