Affine space exercise

[small portal]

I'm trying to solve this exercise, but the first 2 questions are quite confusing. I mean the afdine space is already defined by that function, what am I supposed to do?

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[velvet heart]

for a) given all this

you have to show that you have an affine space of direction E

for b) you do the converse, assuming you have an affine space, show that theta is a well defined map and satisfies all of the above

@small portal

and I imagine c) is about proving all the conditions given in 1. and hence resulting in an affine space due to a)

[small portal]

Ok thx

[versed plover]

@small portal has given 1 rep to @velvet heart

[small portal]

But we defined the affine space by the existence of a function that satisfy those conditions. So, I don't what I still have to do to prove it if it's already defined.

[velvet heart]

show that all of this

satisfies all of this

[small portal]

Ik
But what's the point of doing it in a

[velvet heart]

because you have to prove this is sufficient for affinness

you don't know that before

[velvet heart]

of course, you can show in c) directly by definition that H is affine

but that depends on how affiness is defined in your course

[small portal]

Got it thx

+close