/sci/ - Science & Math

>>10557587
pic
>>10557791
whats wrong with his face?

>>10521717
trying posting instead in the /eng/ thread then

6/?

>>9807308
>Programming in Mathematica
That's a clever way to start a YLYL thread

being a prof. you get to
>work nonstop and be poor for about 5 years as a grad student
>be slightly less poor for 2-3 more years as a postdoc
>be slightly less poor than that as an associate professor for 5 more years until you get tenure
>get tenure but never get funding
seems based to me

This is now a YLYL thread

>>9210619
This

>>8483450
You can post global warming troll stuff, just make it funny. That's the issue here. These are the kind of things a 40 yearold office worker would post on his cubicle wall.

>The proof is left as an exercise to the reader.
>(Why?)
>The proof is obvious and is therefore omitted.
>The other case is similar and left as an exercise.
>(Exercise): Do this.
>Convince yourself that...
>It is obvious that...
>A simple argument yields...

In the college I go to, the first year of all engineering degrees is the same (as in, we all have the same courses). So now I have one year to decide what kind of engineering I want to go into.
Help me pick /sci/.
I'm mostly leaning towards Engineering Physics, but I know /sci/ won't like this.

dumping

i've got a bunch of free time and a huge repertoire of algebraic geometry and number theory stuff

where do i start with IUTT?
i know mochizuki uses a bunch of stuff he introduced in previous papers, but i can't make heads or tails of any of it

i just need a starting point
anyone know?

I haven't constructed the numbers in a while. seems like a good opportunity to practice /sci/ latex

I'll work through it a few ways

Without Peano first:

Define the set of primitive natural numbers [math] \mathbb{N} [/math] as a set containing the empty set, and for each element [math] x [/math] in [math] \mathbb{N} [/math], the set [math] \{ x \} [/math] is also in [math] \mathbb{N} [/math]
so now [math] \mathbb{N} [/math] looks like [math] \{ \emptyset , \{ \emptyset \} , \{ \{ \emptyset \} \} \ldots \} [/math]
now define a function
[math] \mathbf{S} : \mathbb{N} \longrightarrow \mathbb{N} [/math]
by
[math] \mathbf{S}(x) \mapsto \{x\} [/math]
this is called the successor function, and in terms of numbers, it's a function that just adds 1 to x
you can define the natural numbers without the following notation, i'm just using it for convenience
the reason you would want to avoid this in a rigorous construction seems obvious: you're using numbers when they haven't been made yet
anyway
define [math] x^{n} \text{ for } x \in \mathbb{N} [/math] like this:
[math] x^{0} = x, ~x^{n} = \mathbf{S}(x^{n-1}) [/math]
this is just a convenient way to denote repeated succession
now define
[math] + : \mathbb{N}^{2} \longrightarrow \mathbb{N} [/math]
as such:
[math] (x+y) \overset{ \underset{ \mathrm{ def } } { } } { = } (+(x,y)) \mapsto x^{ y } [/math]
this reads: x+y is definitionally equal to +(x,y). x+y is the result of calling the successor function on x, y times

the natural numbers together with this addition operator form a semigroup, which isn't too important yet, but should be kept in mind
now if you're a pleb you'll probably have a hard time with the next part, where i construct the integers

the reason i'm constructing the numbers here is to provide a construction and show that it fits with your intuition properly, so i can prove that 1 = 1 intuitively

post is too long, should i continue or go to sleep?

>oh lord odin please let my latex work