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General Tech Learning Aids/Tools 2 years ago
Posted on 16 Aug 2022, this text provides information on Learning Aids/Tools related to General Tech. Please note that while accuracy is prioritized, the data presented might not be entirely correct or up-to-date. This information is offered for general knowledge and informational purposes only, and should not be considered as a substitute for professional advice.
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If i have a function,
Does it make sense to say the following:
For x∈Xx∈X and y∈Y,y∈Y,
ff is not surjective if f(x)≠yf(x)≠y for some y∈Yy∈Y.
And ff is not injective if f(x)=f(x′)f(x)=f(x′), where x≠x′x≠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?
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 x′x′ with x≠x′x≠x′ and f(x)=f(x′)f(x)=f(x′).
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