/sci/ - Science & Math

A good morning /mg/!

>>11618700
Some comments again:
(25) It is the exponential function indeed. This will be important later when you have the additive group of reals and the multiplicative group of positive reals. This will then give a homomorphism, or a function compatible with the operations of those groups. This is not unique, though. Any a>1 can be used as the base. The inverse is merely the a-base log.
(27) In (a) f is indeed a constant function. In (b) g is constant. These would hold for any composable functions, not just from S to S. You mentioned the special case S={x}. Note that f is then necessarily f(x)=x, so that is not a counter example!
(28) Correct.
(30) That is not wrong. For a finite set S, a function from S to S is injective iff surjective (onto) iff bijective. Try doing (29) to confirm this.
Otherwise good job!

>>11618887
My diary, desu.

>>11618529
>Isn't this the same as Γ\H, as in https://en.wikipedia.org/wiki/Modular_curve?
Yes but with the ambiguity added by the fact that the normaliser of a subgroup contains the subgroup itself, and so it is unclear from the notation whether it is the set difference or the orbits of the conjugation action.