when is it more appropriate to use an implies symbol '=>' vs. a such that symbol ':' vs. a therefore symbol ':.'
#query about mathematical syntax
vague widget
cloud flax
therefore is to like state a result that you arrive at
such that is for a condition
it can be used in sets
for example
S = {2m: m E Z}
vague widget
Oh, I see, thanks, and when do I use a 'then' symbol '=>' vs. an 'if and only if' symbol '<=>'
cloud flax
iff just means 'if' but it goes both ways
vague widget
So, therefore is for a big result
vague widget
iff just means 'if' but it goes both ways
yeah, but often, my steps are just simplifying, there is no real implication
e.g. 5 - a = 3b then 5=3b+a
vs.
5 - a = 3b iff 5=3b+a
also when to use 'so' vs 'then'?
vague widget
yeah, in papers I seem to see only the forwards arrow
is it because the backwards arrow, while, true, is irrelevant
bcs we dont need to go backwards
vague widget
thanks, makes sense, what do u think ab 'so' v 'then'?
cloud flax
hmm
vague widget
also where does 'so/then' fit into all of this
cloud flax
then is usually incorporated into if statements
A => B means if A (holds/is true) then B
it can also be used like this
say I want to prove that the sum of two odd numbers n and m is even
I'd start it like this
Let n = 2k + 1, where k E Z
Let m = 2p + 1, where p E Z
Then,
n + m = 2k + 2p + 1 + 1
=> 2(k + p + 1)
and u finish it
stoic glacier
Silly goose doesn't have maths symbols on his keyboard
cloud flax
im on laptop using a qwerty keyboard mate
stoic glacier
Not even azerty smh
cloud flax
qwerty on top
cloud flax
err
i guess
once u start using these words more in proofs
you kinda just get the hang of it
vague widget
Hows the math here, did I use symbols correctly?
cloud flax
and you'll know what to use where
cloud flax
i forgot this
vague widget
exept for the fact that i did the math wrong 💀