/sci/ - Science & Math

>>9451023
>What exactly is your point?
Some anon said that there isn't any first principles, you said there was and they are axioms, my point is axioms are not first principles.

>Why can't we say whatever is *the* first principle is the first principle?
We already do, but anything we say can be a first principle. There are no first principles in the sense that if there were they would have to come before everything. The Peano axioms are very much primordial and basic but there is something under them that is more basic, primordial, 'first'.

>And this is different from physics how?
It's not necessarily, in fact it's the basis of all rational thought. I never even talked about physics; you're putting words into my mouth.

>Physical hypotheses aren't any more "true" than mathematical hypotheses you know
Yes that's true, that's exactly my point.

I am freshman in college doing Logic and Set Theory course. I am 3 months in and i don't know what the fuck is going on in the lectures anymore.
It started kind of easy but after few weeks in, it became the hardest thing i've studied in my life.
I am complete brainlet please recommend me some books or curses that will help understand it and get throught it.

What are /sci/ approved test strategies?

Personally, I like to smoke a little crack before I take my tests. I've got a pretty good dealer, and the stuff helps my clarity.

Their chicken isn't that special.

What's the best book to learning the concepts in ZFC set theory and going about proving the theorems through the axioms of choice?

So I get, if you wanna solve the Entscheidungsproblem, that you want to check if well-formed formulas get accepted by some univerals algorithm. Clearly a finite state machine is a thing, which does such a similar thing, and then also a turing machine does it.
But (maybe historically), what was the intention of creating something (the turing machine), which would write on the string you put in. In the end, this enables us to create wild programs, which do all kinds of things (compute stuff), and which don't just check if some string is accepted.
Was there a problem these were invented for or where they just a byproduct of the search for a better yes/no machine?

So we arrive at the answer...

I'd lie if I told you that I understand this, but here's the answer that a friend mathematician gave to me:

"You can't talk about the cardinality of all kinds of infinities, because there is no such a thing as a set that contains all infinities". In other words, "being infinite" does not define a set. To build new sets you must always start with a previous one, and apply a condition on it. You can't just say the condition and expect that to define a set.

So elementary set theory saved the day! And now I'm exhausted

Do you believe in the reality (real life applicability) of the statements of any form of symbolic logic? That is, do you think the idea of symbolic representation of drawing conclusions corresponds to "real life". Is some logic valid.

How many kinds of different infinities are there?

By "different" I mean with different cardinality

Let's have some obscure math/science jokes