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I disagree with a merge. Yes, these are related functions, actually both of them work by f(x)=x. However, the two articles look at the matter from a very different perspective. Typically one uses inclusion maps when one thinks of embedding a space into another, bigger space. The identity function on
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Your statement is just a very special case of the more general statement regarding vector spaces. That's why I removed it. There is no reason for restricting the integers to be positive. Nor is there a reason for restricting the numbers to be integers. Nor is there a reason for restricting the
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But seriously. I never thought that common facts known by many people would be definitely known as OVERKILL. One problem is how do we give more sources in order to verify the facts, especially for non-readers who would like to check them? This is analogously like giving citations about
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OK, now I see what you mean! I might not be the only reader who get more confused than enlightened by this reference to advanced number theory in an extremely elementary context. How many of your readers do you expect to look for this information under the heading
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Again, in MY opinion the statement doesn't need a reference. But even if you'd disagree, and think it should, then the reference you've provided doesn't state that the identity function is "often denoted" as such. It's just merely an example of the symbol being
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Of course there is a point. Two functions are equal if they have the same domain, same codomain, and same output for given input. So, strictly speaking, you are incorrect; being surjective is part of what the function is about, not part of the codomain.
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But even if you'd disagree, then still the reference you provided does not show that the identity function is "often denoted" as such. It is just a reference that uses the same symbolism. It doesn't mention common use of the symbol whatsoever.
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the other hand shows up when one deals with automorphisms of a given space, and related business. That is to say, it is true that both the identity function and the inclusion map have the formula f(x)=x, but that's all they have in common.
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vectors to be numbers. In every case where multiplication by 1 makes sense, it represents an identity function. See my point ? I don't mind your removing my reference. (Someone might request a reference if I didn't provide it).
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Yes in any algebraic structure which possesses a multiplicative identity, multiplication by that identity will be the identity function, but such functions are not generally called
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is exactly the same thing. The articles should explain that to the reader. There is no mathematical reason to distinguish. There might be a historical reason, I don't know that.
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as "potentially to start an edit war" is ridiculous.. Instead of reverting the edit back again, you should've started a topic in the talk page so we can discuss it further.
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A common form of citation overkill is adding sources to an article without regard as to whether they support substantive or noteworthy content about the topic
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together with the codomain B. Is there any point in distinguishing functions having the same domain and the same values for the same arguments ?
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Oops. My apologies. I thought we were heading on the edit war because we might revert the edits over and over again. Once again, I apologize.
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Could someone, please, explain, in plain
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The identity function is in general not multiplicative. Only in the special case of
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I believe this statement is correct. I don't understand why it was removed. —
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I've rewritten the notation bit a little, and removed the reference to
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have common criteria: it is supported by the sources citing them.
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I changed back to the previous version for the following reasons:
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I don't know about this one. I already explained this problem to
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does not require a reference imho. It it definitely overkill.
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I agree with Oleg, I think these article should stay separate.
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is defined. The term is not, to my knowledge, used outside of
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is about more than just "using a lot of citations"..
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