Timeline for mixing theorem with definition (definition with proof)

8 events

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Oct 18, 2018 at 14:32	comment	added	Iosif Pinelis		@EmanuelePaolini : I think what we are discussing here is a matter of values and, to an extent, taste. To me, clarity at every step is of high value. If you want to make sure your readers know that rational numbers (say) are being introduced here, you can alert them by a sentence or two introducing the statement and/or maybe give such a piece a subsection or subsubsection title, which is what I have now done. It is also possible to use labels such as "Theorem-Definition", as suggested by S. Carnahan, but I have never seen that in publications.
Oct 18, 2018 at 14:18	history	edited	Iosif Pinelis	CC BY-SA 4.0	added 148 characters in body
Oct 18, 2018 at 10:48	comment	added	Emanuele Paolini		Yes, this is what I'm also currently doing. However I think that in cases like this the statement is more a definition than a proposition. If the reader wants to know how rational numbers are defined he will look for a definition. The fact that a proof is contextually required is incidental, in my opinion.
Oct 17, 2018 at 15:52	history	edited	LSpice	CC BY-SA 4.0	Removed spurious line break
Oct 17, 2018 at 14:31	history	edited	Iosif Pinelis	CC BY-SA 4.0	added 11 characters in body
Oct 17, 2018 at 13:34	history	edited	Iosif Pinelis	CC BY-SA 4.0	deleted 1 character in body
Oct 17, 2018 at 13:16	history	edited	Iosif Pinelis	CC BY-SA 4.0	added 135 characters in body
Oct 17, 2018 at 13:06	history	answered	Iosif Pinelis	CC BY-SA 4.0