Changes

:::I'm not sure I see the "crucial difference" you're seeing. I don't know what you mean by saying that homomorphisms  "allow[] groups that are different . . . to be treated as equal." What do you mean by "treated as equal"? Obviously, if a homomorphism exists between two groups it shows that there are certain structural similarities between the two groups, but this hardly means that they are equal. The fact that 124 and 490 are both even shows that there are certain similarities between them (namely that each includes 2 in its prime factorization), but that doesn't mean we treat them as equal and it certainly isn't evidence that evenness is the result of some sort of liberal bias. <small>Also, I think you have your examples backwards. Bat (animal) is a homophone with bat (sports) because both are pronounced the same but have different meanings. Wind (air flow) is not a homophone with wind (watches) because the pronunciation differs. They are, however, homographs.</small> --[[User:JustinD|JustinD]] 01:23, 26 February 2012 (EST)

:::I'm not sure I see the "crucial difference" you're seeing. I don't know what you mean by saying that homomorphisms  "allow[] groups that are different . . . to be treated as equal." What do you mean by "treated as equal"? Obviously, if a homomorphism exists between two groups it shows that there are certain structural similarities between the two groups, but this hardly means that they are equal. The fact that 124 and 490 are both even shows that there are certain similarities between them (namely that each includes 2 in its prime factorization), but that doesn't mean we treat them as equal and it certainly isn't evidence that evenness is the result of some sort of liberal bias. <small>Also, I think you have your examples backwards. Bat (animal) is a homophone with bat (sports) because both are pronounced the same but have different meanings. Wind (air flow) is not a homophone with wind (watches) because the pronunciation differs. They are, however, homographs.</small> --[[User:JustinD|JustinD]] 01:23, 26 February 2012 (EST)

::::Haha you are absolutely right, my apologies.  I thought I had picked a word specifically with no homophones.  Allow me to elaborate: saying that 124 and 490 are both even emphasizes similarities which is fine.  But consider a statement like "there is only one group of order 3."  There are clearly many, because you can define one on any set with 3 elements.  Nevertheless, you will never hear discussion of the many different groups of order 3, they are all lumped together because of homomorphisms.  Compare this with the professor value of refusing to distinguish between men and women.  To say men and women are both children of God is to discuss similarities while acknowledging differences, as in saying 124 and 490 are both even.  To say men and women are basically the same, as universities today do, is consistent with saying that groups are essentially the same.  I hope that clarifies what I was struggling to say before. --[[User:Bogart12|Bogart12]]

::::Haha you are absolutely right, my apologies.  I thought I had picked a word specifically with no homophones.  Allow me to elaborate: saying that 124 and 490 are both even emphasizes similarities which is fine.  But consider a statement like "there is only one group of order 3."  There are clearly many, because you can define one on any set with 3 elements.  Nevertheless, you will never hear discussion of the many different groups of order 3, they are all lumped together because of homomorphisms.  Compare this with the professor value of refusing to distinguish between men and women.  To say men and women are both children of God is to discuss similarities while acknowledging differences, as in saying 124 and 490 are both even.  To say men and women are basically the same, as universities today do, is consistent with saying that groups are essentially the same.  I hope that clarifies what I was struggling to say before. --[[User:Bogart12|Bogart12]]

:::::They key point you are missing, however, is that in many, many subjects, such as in mathematical aptitude, there is no functional difference between men and women. So yes, in many, many situations, women and men are essentially the same.[[User:KenShomer|KenShomer]] 15:15, 26 February 2012 (EST)

:::::They key point you are missing, however, is that in many, many subjects, such as in mathematical aptitude, there is no functional difference between male and female. So yes, in many situations, women and men are essentially the same.[[User:KenShomer|KenShomer]] 15:15, 26 February 2012 (EST)