Timeline for Given a sequence defined on the positive integers, how should it be extended to be defined at zero?
Current License: CC BY-SA 2.5
4 events
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| Oct 19, 2009 at 16:48 | comment | added | Qiaochu Yuan | Fair enough. I do like that you mentioned universal properties, since my own response to this question is basically "categorify until it becomes obvious what to do." For example, the product of zero things in a category is a terminal object and the coproduct of zero things is an initial object. | |
| Oct 19, 2009 at 14:48 | comment | added | Andrew Critch | I have a utilitarian view on definitions: they're meant to shorten arguments. So whichever properties allow you to shorten your arguments are the "right" ones. This obviously depends on the kind of math you're doing, and how you've been doing it, but I don't think this dependency is meant to be avoided. | |
| Oct 19, 2009 at 7:18 | comment | added | Qiaochu Yuan | This may also sound lame, but how do you know you're looking at the right properties? | |
| Oct 19, 2009 at 7:16 | history | answered | Andrew Critch | CC BY-SA 2.5 |