I'm self-studying Spivak right now and I don't qui

>>8484645
All you need to prove is that the thing on the left of line 3 is equal to the thing on the right.
What you did is assume it was equal and fiddle it around until you got something obvious. Not only is this (technically) wrong, it's a waste of time because you don't need to touch the right hand thing ever.

His answer is essentially just the same steps as the left hand side of your chain except he didn't expand everything into a mess for no reason.

>>8484673
Its not wrong if all the operations are invertible, which they obviously are.

>>8484645
All things done to solve this are essentially the same, just show the n+1 version is true, given the n one is. Its a purely algebraic exercise.

>>8484702
Not wrong in the specific case where you only use a string of invertible operations, no. But it's wrong in general, somebody who (likely) does not know precisely what an invertible operation is will not be aware to guard against errors when they do show up, and it's a trash way of writing mathematical proofs.

LHS = RHS is a common core meme

>>8484702
it's wrong because your conclusion is not what you're trying to conclude

you're trying to conclude [statement] yet what you're doing is assuming [statement] and concluding something different

>>8484645
>self-studying Spivak
do you also lash and cut yourself?

>>8485482
>it's too hard m8
>just relax and vape like me ;^)