Surjective function reasoning.

General Tech Learning Aids/Tools 2 years ago

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manpreet Tuteehub forum best answer Best Answer 2 years ago

If i have a function,

f:XYf:X→Y

Does it make sense to say the following:

 

For xXx∈X and yY,y∈Y,

ff is not surjective if f(x)yf(x)≠y for some yYy∈Y.

And ff is not injective if f(x)=f(x)f(x)=f(x′), where xxx≠x′.

First time learning about functions in such a formal way and I don't have very detailed notes to learn off. p.s, any text recommendations which may aid my understanding about this topic and the basis of analysis in general?

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manpreet 2 years ago

What's really missing from your statements are quantifiers, without which it's hard to define these things. It's correct to say that ff is not surjective if there exists some yy for which there does not existany xx with f(x)=yf(x)=y.

Similarly, ff is not injective if there exist some xx and xx′ with xxx≠x′ and f(x)=f(x)f(x)=f(x′).


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