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Mar
7
revised Natural uses for the co-product of sets?
edited tags
Mar
7
revised Natural uses for the co-product of sets?
deleted 4 characters in body
Mar
7
revised Natural uses for the co-product of sets?
deleted 4 characters in body
Mar
7
revised Natural uses for the co-product of sets?
added 282 characters in body
Mar
7
revised Natural uses for the co-product of sets?
added 282 characters in body
Mar
7
revised Natural uses for the co-product of sets?
deleted 5 characters in body
Mar
7
revised Natural uses for the co-product of sets?
added 303 characters in body
Mar
7
comment Natural uses for the co-product of sets?
@MJD: I think that tagging may be an inessential "implementation detail", an artifact of adopting a "synthetic", as opposed to an "analytic", point of view; I've written at length about this in an "Epilogue" to my original question.
Mar
7
revised Natural uses for the co-product of sets?
added 4744 characters in body
Mar
7
revised Natural uses for the co-product of sets?
added 4744 characters in body
Mar
3
accepted Natural uses for the co-product of sets?
Mar
3
revised Looking for proof of monicity of co-product insertions
added 2 characters in body; edited title
Mar
3
asked Natural uses for the co-product of sets?
Mar
3
reviewed Approve suggested edit on The following subset is a subspace of $\mathbb{R}^2$
Mar
3
reviewed Reject suggested edit on Intuition behind failure rate.
Feb
7
comment Why isn't $\langle a ; a^2 \rangle$ (or $\langle a;a^3, a^7\rangle$) a presentation of $C_4$?
@anon: I see your point. Also Callus just pointed out an even bigger hole in my reasoning. I think that I can straighten out the mess in my head now. Thanks again.
Feb
7
comment Why isn't $\langle a ; a^2 \rangle$ (or $\langle a;a^3, a^7\rangle$) a presentation of $C_4$?
@Callus: OK! I see! That's it. Thank you!
Feb
7
comment Why isn't $\langle a ; a^2 \rangle$ (or $\langle a;a^3, a^7\rangle$) a presentation of $C_4$?
@anon: the book (whether correctly or not) writes "...use $b^8$ and $b^{12}$ as defining relators, and show that $b^4$ can be derived. Hence, by the preceding exercise [i.e. exercise 4], $b^8$ and $b^{12}$ are a set of defining relators." Are you saying the book is wrong, or are you saying that I am misinterpreting it? (I figure it's the latter, but if so I have to concede that I just don't get it, and that it's completely beyond my ken.) Anyway, thanks for your patience. (And likewise to Callus too.)
Feb
7
comment Why isn't $\langle a ; a^2 \rangle$ (or $\langle a;a^3, a^7\rangle$) a presentation of $C_4$?
@Callus: You may be right. I find the text very vague on the subject of picking relators. For one thing, it discusses the defining of relators in terms mappings from sets of symbols to group elements. If one uses the mapping $a \mapsto 2 \in \mathbb{Z}_4$, then $a^2 = 1$ (i.e. $2 + 2 = 0$ in $\mathbb{Z}_4$), so $a^2$ is a relator of the cyclic group of order $4$. And I can derive $a^4$ from it.
Feb
7
comment Why isn't $\langle a ; a^2 \rangle$ (or $\langle a;a^3, a^7\rangle$) a presentation of $C_4$?
@anon: the "then by exercise 4 blah blah" bit comes basically verbatim from the book. You can see the exact quotation in my post.