I look forward to your math pictures! Thank you for them. Please tell me where I am going wrong here, about the badly behaved functions. I think the sketch is about a variety of inputs all giving the same output, right? So that is a horizontal line, and this is a perfectly fine function. Why is it behaving badly?
MrHonner
· February 20, 2014 at 9:32 am
Hi Laura-
You are right, this is a legitimate function. The joke is that the best-behaved functions are one-to-one. Behaving in this many-to-one manner makes certain aspects of the function difficult to deal with.
And I’m glad to hear you enjoy the photos! Thanks for letting me know.
Andy Huynh
· February 21, 2014 at 2:10 pm
It’s better to have functions that are one-to-one and onto so that there can be an inverse function. One-to-one is a better property because if a function is not onto, you can force it to be onto by restricting the codomain to its range. Now sometimes that’s easier said than done because sometimes you don’t know a function’s explicit range.
A celebration of today’s ambigrammatic date*. *Celebration only applies for those who use the DD/MM/YYYY date format. Related Posts 02022020 81818 8/15/17 12/12/12 11/11/11
In most ways this is a sorrowful triangle, but on this day it was remarkably beautiful. Related Posts Math Photo: Shadows and Triangles Math Photo: Blue Buckyball Photography
3 Comments
Laura Sosnowski · February 19, 2014 at 7:20 pm
I look forward to your math pictures! Thank you for them. Please tell me where I am going wrong here, about the badly behaved functions. I think the sketch is about a variety of inputs all giving the same output, right? So that is a horizontal line, and this is a perfectly fine function. Why is it behaving badly?
MrHonner · February 20, 2014 at 9:32 am
Hi Laura-
You are right, this is a legitimate function. The joke is that the best-behaved functions are one-to-one. Behaving in this many-to-one manner makes certain aspects of the function difficult to deal with.
And I’m glad to hear you enjoy the photos! Thanks for letting me know.
Andy Huynh · February 21, 2014 at 2:10 pm
It’s better to have functions that are one-to-one and onto so that there can be an inverse function. One-to-one is a better property because if a function is not onto, you can force it to be onto by restricting the codomain to its range. Now sometimes that’s easier said than done because sometimes you don’t know a function’s explicit range.