One is surjective and the other isn't, but according to the set-theoretic definition of a function (a function is equal to its graph) they're equal. $\endgroup$ – Akiva Weinberger Commented Sep 3, 2015 at 21:57

Understanding the definition of surjective function. Ask Question Asked 7 years, 3 months ago.

Definition of a surjective morphism of schemes. 2. Definition of proper morphism between schemes. 2. Etale ...

2018年3月6日 · We sometimes use the triple of the definition specifically because we want to associate the codomain to the function; the statement that "a function is surjective" then makes sense without explicating a codomain, and it also has real implications (like the …

Intuitive definition of injective, surjective and bijective. Ask Question Asked 7 years, 3 months ago.

2015年5月14日 · As to whether it is a surjective function, the answer is no, since 1, an image, has 3 distinct pre-images in the domain. $\endgroup$ – Kevin Zakka Commented May 14, 2015 at 13:46

2020年4月3日 · Graphically, it seems that surjective functions have the codomain and the image equal to one another. But, working only with the definition of surjectivity, I can only understand how the all quanti...

2013年7月15日 · What you're (probably) looking for is the negation of the definition of surjective. To find the negation, remember that "for alls become there exists" and "there exists become for alls".

$\begingroup$ @poorna: The stalks being surjective does not imply that the map on global sections is surjective. This is indeed the content of the Caution I referenced in my answer. This is indeed the content of the Caution I referenced in my answer.

2020年11月7日 · I am in a Proof writing class and we are currently on functions. I have a good understanding of what it means to be injective or surjective in terms of elements in the set but I am having trouble coming up with a formal definition that just generalizes the definitions in terms of sets using an iff statement.