Timeline for Can a mathematical definition be wrong?
Current License: CC BY-SA 2.5
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 2, 2010 at 12:18 | comment | added | gowers | @Stefan, there is no function from a non-empty set to the empty set. (Not even "the empty function".) | |
| Dec 2, 2010 at 9:01 | comment | added | Stefan Geschke | @Tom Goodwillie: What is the problem with a function with empty domain? This is the empty function, which is 1-1, and its left inverse is the empty function itself (composition of the two functions is the identity on the epmty set, which is again the empty function). | |
| Dec 2, 2010 at 1:00 | comment | added | Joel David Hamkins | It seems inaccurate to portray the logician's standard definition of function as an amusing failed attempt at precision. Although other definitions are also common, this particular definition is used with consistency and precision throughout logic and set theory and other areas, including introductory undergraduate texts. (There are no problematic issues with surjections, bijections or inverse functions.) The link in JBL's comment has further explanation. | |
| Jul 14, 2010 at 6:22 | comment | added | Harry Gindi | @gowers: Many set theorists actually define a function this way. | |
| Jul 12, 2010 at 22:58 | history | edited | gowers | CC BY-SA 2.5 |
Removed accidental repetition
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| Jul 12, 2010 at 15:36 | comment | added | Tom Goodwillie | In one undergraduate text on algebra the domain of a function is required to be nonempty. I think the author wrote this in order to be able to assert later on in the book that every one to one function has a left inverse. | |
| Jul 12, 2010 at 12:19 | comment | added | JBL | There was a discussion of this point here very recently: mathoverflow.net/questions/30381/definition-of-function | |
| Jul 12, 2010 at 7:09 | history | answered | gowers | CC BY-SA 2.5 |