I know this is really trivial, but I got stuck about how to prove it
#prove that if m is odd, then m squared is odd
civic venture
I can define the universe and what a odd number is, but im stuck trying to prove that m squared is odd
brisk python
For something to be even, it'd have to be divisible by 2. Multiplying an odd number by another wouldn't include a 2
civic venture
For something to be even, it'd have to be divisible by 2. Multiplying an odd num...
what do you mean a number including a 2?
as a factor?
brisk python
Yeah
civic venture
odd number m satisfy m = 2k + 1
m^2 = 4k^2 + 1
I assumed p of p => is true
I just need to prove p => q and the rest clicks
brisk python
4k^2+4k+1 I think
civic venture
4k^2+4k+1 I think
where did you get the second term?
brisk python
So, 4k^2+4k can be rewritten as 2(2k^2+2k), showing it's equal to 2k_1. Then you have the plus 1, making it 2k_1+1, so it's odd
brisk python
where did you get the second term?
(2k+1)(2k+1)
civic venture
4k^2+4k can be rewritten as 2(2k^2+2k), showing it's equal to 2k_1.
hold on'
how is the second expression related to 2k_1?
brisk python
Replacing (2k^2+2k) with k_1
civic venture
and where did you get the +1?
brisk python
4k^2+4k+1 I think
From this
civic venture
so you did variable magic and you proved m^2 is odd
neat
but you forgot something
this proof isn't a proof without those three letters
brisk python
Honestly, I'm not really sure how to write proofs
It's something I should probably teach myself at some point, but I haven't gotten the chance to
civic venture
how good are you at math?
brisk python
I dunno, I'm decent compared to my schoolmates, but in comparison to a lot of other people I'm still at the beginning of my journey into math
civic venture
I can say the same
My dream is to build math from the ground up again
even tho godel proves that is this just a dream
but i'll try regardless
brisk python
Yeah, that's a good mindset, I honestly don't entirely believe the incompleteness theorem
Oh, you're in middle school
It's really cool that you're thinking about advanced mathematics now, I'm sure you'll go a long way
civic venture
Yeah, I have a book in discrete maths for computer science
and other math books
(I have 3 and will get more)
brisk python
Computer science is really useful within math, it's good that's you're starting on it now
But yeah, I'd definitely recommend the books I mentioned in the other chat, they have some really interesting concepts
brisk python
HaikuBot is fun
civic venture
best of luck to you, fellow mathematician