Timeline for Do almost all systems of quadratic equations have solutions?
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 18, 2017 at 20:08 | vote | accept | glS | ||
| Oct 26, 2017 at 11:47 | comment | added | Gerry Myerson | Existence of a small change is not equivalent to measure zero. E.g., given any irrational, there's an arbitrarily small change that makes it rational, but the irrationals have full measure. | |
| Oct 26, 2017 at 11:36 | comment | added | glS | @GerryMyerson oh right of course. I meant to say that there exists a small change such that (...), which should be equivalent to say that the set of non-solvable systems has measure zero (in some properly defined metric over the parameters). I'll fix that bit | |
| Oct 26, 2017 at 11:34 | comment | added | Gerry Myerson | Even in the linear case, if $A$ is singular, there exist arbitrarily small changes that keep it singular. E.g., multiply it by $1+\epsilon$ for $\epsilon$ arbitrarily small. | |
| Oct 26, 2017 at 11:22 | comment | added | glS | @GerryMyerson care to expand a little bit? Isn't this in contrast to Igor's answer? | |
| Oct 25, 2017 at 22:07 | comment | added | Gerry Myerson | "is it always true that an infinitesimal change of parameters will give me a system which has solutions?" It is always true that there exists an infinitesimal change, etc., etc.; it is not always true that every infinitesimal change etc., etc. | |
| Oct 25, 2017 at 14:55 | answer | added | Igor Rivin | timeline score: 16 | |
| Oct 25, 2017 at 14:00 | history | edited | glS | CC BY-SA 3.0 |
added 1 character in body
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| Oct 25, 2017 at 13:53 | history | asked | glS | CC BY-SA 3.0 |