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/sci/ - Science & Math

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9230176 No.9230176 [Reply] [Original]

I literally wanna learn the foundations of arithmetic and algebra, with autistic masturbation and formalization, i want the most solid foudnation for my arithmetic and algebra knowledge, where should i start?

>> No.9230177

>>9230176
principia mathematica

>> No.9230180

>>9230176

Landau Foundations of Analysis

>> No.9230186

>>9230176
heidegger

>> No.9230196

>>9230186
what

>> No.9230209

>>9230196
you heard me

>> No.9230251

Here are the rules for natural deduction:
1. We can stipulate anything conditioned on assumption
2. From P and P -> Q, we can conclude Q
3. From P, we can deduce (P or Q) for any Q
4. From P and Q, we can deduce (P and Q)
5. From (P or Q), P -> R and Q -> R, we can deduce (P or Q) -> R
6. We can discharge assumption P for conclusion Q by deducing P -> Q no longer conditioned on P
7. From (P and Q) we can deduce P or deduce Q
8. From not (not P) we can deduce P
9. From a contradiction we can deduce the negation of any assumption that leads to contradiction
10. If we prove P(a) for arbitrary 'a', we can deduce P(x) for all x
11. From P(x) for all x, we can deduce P(a), for any a.
12. From P(a), we can deduce P(x) for some x.
13. From P(x) for some x, if we prove Q from P(a) where Q does not involve 'a', then we can deduce Q from P(x) for some x.

All else is a trivial exercise for the reader

>> No.9230274
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9230274

>>9230176
You should go to community college and take an algebra course. It will show you all of the basics at once,if you aren't a brainlet. If you can't ace everything up to Calc 1 then maybe consider installing pipes in basements for the rest of your life.

>> No.9230284
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9230284

>>9230176
>i want the most solid foudnation for my arithmetic and algebra knowledge

Well bud, you're going to have to start with the real foundations. Find a textbook that deals with the ZFC axioms rigorously, targeted at an advanced undergraduate or first year graduate level.

Foundations of Mathematics, by Kenneth Kunen might be good.

>> No.9230972

>>9230284
thank you

>> No.9231106
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9231106

>>9230176
Start with this and work your way up.

>> No.9231113

>>9230284
>not starting with topos theory

drop out, brainlet

>> No.9231233

>>9230176
N.Bourbaki: éléments de mathématique will be your new friend

>> No.9231270

Go more abstract, probably go through group, ring or topos theory, followed by category theory

>> No.9231622

>>9230274
That's not what he means fuckass

>> No.9232076
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9232076

>>9231270
>learn topos theory, followed by category theory

>> No.9232944

>>9230274
You are beyond help

>> No.9233195

>>9230274
I found an asshole. Morsor est morsor de morsori.
Non moral in exego intent. Ego revelere in futur. In pictur est secret pictur. Non fals informar ergo non /x/.

>> No.9233201

>>9230274
Non similar de zodiac. non informarie in crypt

>> No.9233215

>>9230176
>A book on proofs
Book of Proof by Hammack (http://www.people.vcu.edu/~rhammack/BookOfProof/))
>A book on set theory
Elements of Set Theory by Enderton
>A book on number theory
An Introduction to the Theory of Numbers by Niven, Zuckerman, and Montgomery
>A book on linear algebra
Linear Algebra Done Wrong by Treil (http://www.math.brown.edu/~treil/papers/LADW/LADW.html))
>A book on abstract algebra
http://4chan-science.wikia.com/wiki/Mathematics#Abstract_Algebra