you can put it in off-topic, and I just finished gr10 math, so no idea, sorry
Computer Science Canada discrete math |
| Author: | matt271 [ Wed Apr 08, 2009 7:35 pm ] |
| Post subject: | discrete math |
there is no math section so i didnt know where to post this. anywaysssssss i am just wondering if anybody can explain how to show two graphs are isomorphic? i dont have the text book. but i did google it and i found this Wikipedia page http://en.wikipedia.org/wiki/Graph_isomorphism i did it exactly like this example, but on my midterm the teacher took away points. i went to ask why he took away points but there is a language barrier with this teacher. all i gathered is that he wanted me to define some function like "f : a -> b" but i have never seen this format before. my exam is tomorrow just wondering if anybody can explain it real quick?? this is a different question then was on my midterm but i think its more interesting because there's no graph: Let T = {x|x divides 3} show that (T, +) and (Z, +) are isomorphic. can i just say f(n) = 3n , n belongs to Z ? ty |
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| Author: | saltpro15 [ Wed Apr 08, 2009 7:55 pm ] |
| Post subject: | RE:discrete math |
you can put it in off-topic, and I just finished gr10 math, so no idea, sorry |
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| Author: | matt271 [ Wed Apr 08, 2009 8:07 pm ] |
| Post subject: | Re: RE:discrete math |
saltpro15 @ Wed Apr 08, 2009 8:55 pm wrote: you can put it in off-topic, and I just finished gr10 math, so no idea, sorry
got me all excited for nothing 
haha |
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| Author: | Tony [ Wed Apr 08, 2009 8:20 pm ] |
| Post subject: | Re: discrete math |
matt271 @ Wed Apr 08, 2009 7:35 pm wrote: he wanted me to define some function like "f : a -> b" but i have never seen this format before.
It's a one-to-one (injective) function. If you also define "f2 : b -> a" (onto (surjective)) then f and f2 create a bijection, which shows isomorphism of a and b. |
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| Author: | matt271 [ Wed Apr 08, 2009 9:24 pm ] |
| Post subject: | RE:discrete math |
k i got it ty ty  |
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| Author: | Brightguy [ Thu Apr 09, 2009 3:31 am ] |
| Post subject: | Re: discrete math |
Tony @ Wed Apr 08, 2009 8:20 pm wrote: It's a one-to-one (injective) function. If you also define "f2 : b -> a" (onto (surjective)) then f and f2 create a bijection, which shows isomorphism of a and b.
This shows |a| <= |b|. A bijection is a single function (one that is injective and surjective). matt271 @ Wed Apr 08, 2009 7:35 pm wrote: Let T = {x|x divides 3} show that (T, +) and (Z, +) are isomorphic.
Well, you mean T = { x | 3 divides x }. You have to give a bijective function f: Z -> T which preserves the addition structure, i.e., f(a+b)=f(a)+f(b). You've found f, you just have to show it satisfies the necessary properties. One way to show f is bijective is to give its inverse. LaTeX is broken again? You guys are killing me.  |
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