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I got marked off for some reason

I don't see anything blatantly wrong with it...
I came up with a slightly different argument

What does 2<{5,6,7,8...} mean?

Oh. You mean 2 is less than any element in that set.

right

\[2^k4\)
not sure if your prof would have liked that any better, I'm not so great at induction...

well I guess you could proceed to multiply both sides by k! again but that seems a bit redundant

Turing I like that you recalled that k+1>2 since k>=4
So
\[2^{k+1}=2^k \times 2

This proves the thingy

yes, much more succinct myin :)

You can say that middle part was by induction when I used 2^k

Or turing
I and turing or interchangeable I guess

are*

i managed to eke out a 12/10 on the homework nonetheless :)

then quit yer whining :P

at least that has been all the examples that the teacher has done on the board for us

i was finally able to parse thru your proofing. I like it.

ah, so I should try to work the 2^k < k! up to it, instead of backtracking back down

ah, so I should try to work the 2^k < k! up to it, instead of backtracking back down
yes.

but 2<(k+1)
since k>=4
and 2

oops 2^k

fair point...