User axiomsofchoice - MathOverflow

Discharging assumptions

2009-11-03T10:27:45Z

When constructing proofs using natural deduction what does it mean to say that an assumption or premise is discharged? In what circumstances would I want to, or need to, use such a mechanism?

The reason I'm asking this questions is that many text on logic use this term as understood by the reader and don't take the time to adequately explain the technical sense in which they are using it.

Answer by axiomsofchoice for Origins of Mathematical Symbols/Names

2009-12-09T13:04:07Z

You might like to take a look at this site:

Earliest Uses of Various Mathematical Symbols

Answer by axiomsofchoice for Text for an introductory Real Analysis course.

2009-11-04T09:16:30Z

I'd recommend Hardy's Course of Pure Mathematics. Now in it's 101st year it still remains relevant to modern readers. It takes it bit longer to get to core of real analysis (e.g. limits, continuity, &c., &c.) than perhaps other similar texts do, which tends to make it more suitable as an introductory book, but there's enough there to engage those wanting explore the subjects in more detail.

What are the most important Open Access Mathematics journals at present?

2009-10-30T21:03:08Z

I'm asking this question from the perspective of someone who just wants to read journals rather than contribute to them. For the purpose of this question I'm using the definition of Open Access in the sense of the Budapest Open Assess Initiative:

"By 'open access' to this literature, we mean its free availability on the public internet, permitting any users to read, download, copy, distribute, print, search, or link to the full texts of these articles, crawl them for indexing, pass them as data to software, or use them for any other lawful purpose, without financial, legal, or technical barriers other than those inseparable from gaining access to the internet itself. The only constraint on reproduction and distribution, and the only role for copyright in this domain, should be to give authors control over the integrity of their work and the right to be properly acknowledged and cited." (From the BOAI FAQ)

I'm aware of the mathematics journals listed in the Directory of Open Access Journals but I have no way of finding out from that list which journals are most respected by the community.

Comment by axiomsofchoice

2009-11-30T16:00:43Z

Thanks for this answer Apollo. One way of describing the purpose of discharging assumptions which I liked when I was reading up about this was that it's like introducing a temporary variable in programming - i.e. the scope is limited between the point where it's used in a rule and upwards to where it's discahrged; for example in inductive proofs the induction step requires you to assume P(n=k), showing P(n=k+1) and in doing so discharging P(n=k). (Btw, it's a bit nit-picky I know, but you can only discharge an assumption, not a premise (except when an assumption actually becomes an premise).)

Comment by axiomsofchoice

2009-11-03T01:11:57Z

@Scott I'm not offended - far from it - but I am a little confused about the problems with the wording of this question. I'd be interested to know about your proposed changes - hopefully this might also be instructive for others writing similar questions. Best to continue this discussion via email though (my username at gmail). Don't get me wrong here, I really like what you guys are doing with this site but my guess is that as it (hopefully) continues to grow in popularity you're going to find it increasingly difficult to maintain the high level of editorial standards you've set for yourself.

Comment by axiomsofchoice

2009-10-31T12:12:02Z

@Anton - The question as written is exactly what I wanted to ask - it doesn't matter that I know about it, I want to know what the community respects. In composing it I used "Do good math jokes exist?", "Undergraduate Level Math Books" and "Most interesting mathematics mistake?" as models of what works well as a good mathoverflow question. I fail to see how they differ from the style of my question - are 'good' and 'interesting' less vague than 'important'? It would help if you could add some good vs. bad examples on the faq. As a community wiki it's ok that there's no answer to it (cf. faq).