hi prof walton, i have a quick question

Shoot (but don't hurt me.)

haha, ok so i am under the impression that when functions

say f: x → x that means that the domain and the codomain

are the same but the ranges can be different correct?

say f: x → x that means that the domain and the codomain

are the same but the ranges can be different correct?

The codomain (after arrow) lists the type of numbers

that might be values in the output, while the domain

(before arrow) lists all of the numbers that are in the

list of potential inputs. The range is the list of numbers

that actually are outputs. Is this the question?

yep, so the range is a sub"field" of the codomain ritethat might be values in the output, while the domain

(before arrow) lists all of the numbers that are in the

list of potential inputs. The range is the list of numbers

that actually are outputs. Is this the question?

it lists all possibles while the range is what numbers

are in the function ?

subset instead of sub"field". Otherwise, yes.

haha ya i was lookin for that wordThe cheapest answer for codomain would be simply R

(all real numbers). If the codomain is listed as something

more specific, that helps us understand the function better,

but we still might skip some of the numbers in the set.

ic, so when im looking at f and g that have the same(all real numbers). If the codomain is listed as something

more specific, that helps us understand the function better,

but we still might skip some of the numbers in the set.

codomain, that then would not imply that f(g) = g(f)

because the ranges could be different? or is

f(g) being = to g(f) relational to the domain only

Equality of functions requires that they have the same

domain and the same values at every point in that

domain. If the domain is different, then the functions

must not be equal. If the functions have different

values for any point, then the functions are not equal.

so d → s just means that the domain could producedomain and the same values at every point in that

domain. If the domain is different, then the functions

must not be equal. If the functions have different

values for any point, then the functions are not equal.

these outputs right?

That's right. The outputs must be somewhere in the

list known as S. And the inputs only make sense if they

are in D.

but s just means possible outputs because its the codomain ritelist known as S. And the inputs only make sense if they

are in D.

Yes, because it is the codomain (after arrow)

rite rite rite, gotcha, this stuff is weird
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