>>7998053
>doing it line by line, listing prior statements and axioms

That's terrible

>which can easily be supported by truth tables

That's retarded

It's impossible to really make a mathematical proof 100% rigorous in a practical way. Instead take a cue from the proofs in whatever texts you're studying as to a level of acceptability. For example if you're just beginning to learn algebra or something you might write out all the constructions completely and be very formal with your symbols and formulas. But once you learn more and get used to standard techniques you can just say things like "construct the standard quotient and project down" or "clearly this subset kills all the elements in this other thing" or "such and such because the localization at this prime etc." because people know what you're talking about.

>>7998053
Just stick to the definitions, if you understand the definitions you will know what you have to prove.

>>7998053
just include "it has been shown" or "we leave it to the reader" and boom you are golden

>>7998062
Why is it terrible?

>>7998073
Okay I guess that's fair. It just seems like the level is inconsistent between his answers. I don't want to cheat myself, you know? Ideally I'd go through and relate the changes in equations to the 12 properties or a proof derived in an earlier problem (I'm mostly doing them all in order then cleaning them up into a separate notebook for reference).

There's just stuff like "oh take the square root of both sides" that hasn't been defined and seems like a big hole. My head locks up asking "why am I allowed to take the square root of both sides?" Operations like addition and multiplication are easy to prove as legal but some 'accepted' stuff is beyond me (without induction, at least)

>>7998079
You mean the 12 properties? Like I said prior, there's some stuff that he doesn't cover.

I don't care about saying "i finished Spivak" i just want to be able to exhaustively convince myself of the validity of the math I'm using. Thanks /sci/

>>7998098
Well I din't learn I don't know spivak, I learned calculus (or for you amercians classic analysis) from Fichtenholz, but still I can give you generl protis. I assume that he starts with defining the real numbers (the 12 postulates that you refered to), this part i not crucial for your understaning of calculs, this part part is there to jus formalize the natural intuition about the real line. The thing that you shold actually concentrate on is the definition of convergance of a sequance. Do all the theorems that describe the basic properties of the limit, then you will get some intuition what you shuold do when you are proving stuff in analysis. As for the axiomatic introduction of real numbers it will be actually crucial for proving tha a Cauchy series is convegent, s then there will be a good point to go back to the axiomatic theory of real numbers.

>>7998129
shit im drunkt it should be:

Well I don't know spivak, I learned calculus (or for you amercians classic analysis) from Fichtenholz, but still I can give you general protips. I assume that he starts with defining the real numbers (the 12 postulates that you refered to), this part i not crucial for your understaning of calculs, this part part is there to just formalize the natural intuition about the real line. The thing that you should actually concentrate on is the definition of convergance of a sequance. Do all the theorems that describe the basic properties of the limit, then you will get some intuition about what you shuold do when you are proving stuff in analysis. As for the axiomatic introduction of real numbers it will be actually crucial for proving that a Cauchy sequance is convegent, then there will be a good point to go back to the axiomatic definition of real numbers

>>7998053
By the axiom of idiocy, if you don't know how to write proofs, then you are an idiot.
OP doesn't know how to write proofs.
Therefore, he's an idiot, QED.

>>7998150
Upvoted :)

>>7998168
Thanks memester ;-)))

>>7998137
Spivak has a section or two devoted to arithmetic and order properties on fields so that you can get familiar with proof writing. For most Americans, analysis is the first or second exposure to formal proofs.
>>7998053
OP. Be overly explicit until you feel like you no longer have to be.
My first proofs were filled with associativity and commutativity axioms.
Just do those first couple proofs if you aren't comfortable. That 0 is the multiplication absorbtion element and that the inverse of an inverse is the object, etc
Eventually you'll get bored and look for juicy proofs to stick your chops into.
At least that's how it worked for me.

>>7998053
Mathematical writing is a skill that you'll develop as you read and write more math. Remember the purpose of most proofs is to communicate to other mathematicians and to yourself why a certain proposition is true. You're generally not writing a proof with the purpose of it being checked by a computer.

In general you should write things in plain english; avoid symbols if possible (for example write "for all" instead of [math]\forall[/math]). The biggest mistake I see math newbs do is try to write proofs as a string symbols are incomprehensible to a human reader. Again, unless you're purpose to set up a theorem proving / checking computer program, your goal is to make humans understand what you're talking about.

Understand who your audience is and what they can be assumed to know; it would be stupid to have reprove or reference basic theorems/definitions all the time in order to prove something -- again the goal is communication; if you're doing exercises from a book a good standard is to assume the basic definitions and theorems once you're past that section of the proof. The goal here is that if you read your proof again a year from now, you'll know what you're talking about and be convinced of that the proposition is true.

>>7998236
>section in the book*

Guys i need some help here my english is pretty bad and can't understand the whole video and i need this information. Can someone transcribe what is she saying ?

https://www.youtube.com/watch?v=tSf6wbojFK8&nohtml5=False

Thanks guys i think you pretty much cleared it up for me.

>>7998053
here's a rule of thumb that's a good exercise in studying anyway

As you go from the assumptions, think of what would change if you changed your assumptions. Like, if you have to prove something like very vector field has a basis, think of what goes wrong with rings. Then, you know the kind of thing exactly it is that requires proving. If you find you've exhausted most of the reasonable alternatives (the only things left to check are things like WHAT IF SET THEORY IS WRONG???), then you probably have a pretty complete proof.

A good proof should make it clear exactly the extent to which the assumptions allowed you to come to the conclusion you did, and show what about them made that result possible, such that different circumstances wouldn't necessarily have the same properties.

Hey someone recommend a good logic book

>>7998053
at first you should do EVERY step of the proof rigorously, no english. all logic. do this for a while, you're going to start to see patterns and feel comfortable with arguments, and when this happens, you can start using english to say exactly what you mean.

The book I used is "An introduction to mathematical reasoning" by Peter Eccles.

I thought it was a pretty good book so you might want to check it out OP.