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what is the easiest way to prove a function si one to one? Also to prove it's not one to one...

Define $f : \mathbb{N} \to \mathbb{N}$ by $f(n) = \cdots$. Define $g : \mathbb{N}\times\mathbb{N} \to N$ by $g(m, n) = \cdots$.

For $f$ and $g$ I need to say if it's one to one or not one to one, I'm not sure what kind of values I should expect (it's a very entry level course into discrete mathematics) Would anyone be able to hazard a bit of a guess as to what the values should be?

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    To prove f is a one-to-one function, I'd check whether f(a) = f(b) implies a = b. To prove it not, I'd look for a counter-example. I don't think you need any further expectations/guessing.2011-11-07
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    @jolpi: I am not sure what this question is asking exactly? Do you want us to suggest some exercises, on which you can try your understanding of this notion?2011-11-07
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    @MartinSleziak that would be good if you wouldn't mind.2011-11-07
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    I think the comments you got to your previous question, http://math.stackexchange.com/questions/79399/basic-relation-help apply here, too. Anyway, there are books full of worked exercises. For example, there is a Schaum's Outline on Discrete Mathematics.2011-11-07
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    Perhaps you can find a few exercises by yourself: [exercise "one-to-one" function](http://www.google.com/#q=exercise+%22one-to-one%22+function) or [exercise injective function](http://www.google.com/#q=exercise+injective+function).2011-11-07
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    Yet another non-rude, more or less clear question gets downvotes without pointing out what's wrong with the question.2011-11-07
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    @Gortaur I can fully understand the downvotes. I do not see any real question asked here.2011-11-07
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    @Gortaur: What's *right* with the question?2011-11-07

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