God I love google: late Middle English (originally denoting a short written document): from Anglo-Norman French billette, diminutive of bille (see bill1). The verb is recorded in the late 16th century, and the noun sense ‘a written order requiring a householder to lodge the bearer, usually a soldier,’ from the mid 17th century; hence the current meaning.
@MagicOctopusUrn well I have time during my spare in block 2 and during lunch lol. but yes I do go to school and you'll notice I say "gtg history o/" a fair amount because I code-golf from 7:55 to 8:15 before school technically starts
@LeakyNun I wrote this "requirements system" for my company that uses latex to let actuarials input equations directly into a production system. It's buggy, but really does work better than them like "I guess this is right".
@LeakyNun the biggest stipulation was that they only needed [product, sum, fractions, and like 12 other things]. Then I infer that any non-numerical non-syntactical element is a variable. Then I have my web-ui show fields for each 'variable' element so that when they inpu tthe variable elemetns the equation actually executes.
Was a really neat idea, got my promotion from it.
Honestly "execute simple LaTeX" would be an AMAZING challenge, if anyone wants to steal that.
@TuxCopter are you using an SSD? I've had problems with a sector on an HDD (spinner) not being able to read correctly, making me unable to partition things like I wanted.
I mean, being "even", is divisibility by 2 (a prime), as such, it's prime factors must contain 2. Multiplication can be described as concatenation of prime factors (I have no idea how one would prove this), as such, the prime factors of a×b must atleast contain all the prime factors of a. So if a is even, then a's prime factors contains 2, then a×a's prime factors contains 2, therefore a×a must be even.
the koth starts by auctioning a bunch of cards off, and bots buy up the cards, and then can do trades and stuff. then after that the bots play ccg type games with their collected cards
To prove $P \implies Q$ you can prove $\sim Q \implies \sim P$ - not $Q$ implies not $P$. This is called contraposition. Both statements are equivalent. Here's how we prove the contrapositive.
Let $n = 2j +1$. Squaring gives $n^2 = 4j^2 + 4j + 1 = 2(2j^2 + 2j) +1$. Hence $n^2$ is odd.
This is e...
@LeakyNun I decided to read through your entire proof after realizing that I do actually understand it, just to get familiar with formal logic a bit more / to review :P
Definitions
$x\text{ is even} := \exists y[y+y=x]$ (Denote as $E(x)$)
$x\text{ is odd} := \exists y[S(y+y)=x]$ (Denote as $O(x)$)
Axioms
$\forall x[S(x) \ne 0]$
$\forall x \forall y[S(x)=S(y) \implies x=y]$
$\forall x[x+0=x]$
$\forall x \forall y[x+S(y)=S(x+y)]$
$[\varphi(0) \land [\forall ...
