Anonymous at Wed, 20 Mar 2024 23:28:37 UTC No. 16088809

>homework thread

Anonymous at Wed, 20 Mar 2024 23:31:30 UTC No. 16088811

>>16088806
the label [-a] is short hand for the additive inverse of the label [a], which isn't necessarily negative (i.e. [a] < 0 is not necessarily true)

Anonymous at Wed, 20 Mar 2024 23:41:30 UTC No. 16088828

>he fell for the "Start with Serge Lang's Basic Mathematics™" meme
LOL

Anonymous at Wed, 20 Mar 2024 23:44:22 UTC No. 16088834

>>16088828
Its good

Anonymous at Wed, 20 Mar 2024 23:48:14 UTC No. 16088837

>>16088834
>Its good

Anonymous at Thu, 21 Mar 2024 00:02:22 UTC No. 16088854

>>16088806
a negative number is a number less than 0
a minus sign denotes flipping the value from negative to positive or from positive to negative, -x is not negative because it's value is depend on what x you use.

for x = -3
-x = 3

which can be proven like so:

-3 = (-1)*3
then
-x = (-1)*x = (-1)*(-1)*3

since dividing by 1 is equivalent to multiplying by one we can change the equation into:

-x = (-1)/(-1) * 3

For all non-zero number y: y / y = 1 (or y * y^(-1) = 1), which is also a handy definition of one — a number resulting from diving any number by itself. We get:

-x = 1 * 3 = 3

hence

-x = 3 => there exist such x that -x > 0 => -x is not a negative number

Anonymous at Thu, 21 Mar 2024 00:31:09 UTC No. 16088881

The expression "-a" might be positive if "a" represents a negative number. For example, let "a" represent "-1", then -a=-(-1)=1.

Hold onto that book and never let it go until you finish it.

Anonymous at Thu, 21 Mar 2024 00:34:10 UTC No. 16088883

>>16088881
where does one go after finishing lang's BM?

Anonymous at Thu, 21 Mar 2024 00:54:02 UTC No. 16088903

>>16088883
You have a few choices. Serge Lang is basically a precalc book. The trig section seems a bit thin, so I say do a bit more trig review, or supplement that section with something a bit more in depth if you require it. Only if you require it. Otherwise just move on.

So after Serge Lang, I'd say you can either work through discrete math, linear algebra, or calculus. It doesn't really matter too much which order you do these in imo, although calculus is often done first.

The main thing is to move forward. Once you know the basics, you can sort of pick and choose what interests you, and if you encounter terms you aren't familiar with, learn that as you need it.

My personal recommendation is "Book of Proof" just because it is short, and will get you a feel for proofs which is very important.

Anonymous at Thu, 21 Mar 2024 00:59:58 UTC No. 16088914

>>16088903
Thanks for the advice, anon. NTA but I have a few books about differential and integral calculus and a book about statistics. I've been meaning to go through them for years but didn't have time. When can I delve into them?

Anonymous at Thu, 21 Mar 2024 01:05:17 UTC No. 16088921

>>16088914
Whenever you want, anon. As long as you know the basics you can build from that. The ideas of calculus are not that difficult, the hard part is all the algebraic manipulations and trig identities. So I guess be comfortable with factoring, solving equations, looking at graphs of different functions and identifying them, the trigonometric identities and how to work with trig functions in equations.

Anonymous at Thu, 21 Mar 2024 01:13:27 UTC No. 16088932

>>16088921
Thanks, that makes total sense. Thanks again. I'll make sure to master the basics and after that I'll explore and see what my level is. Well I'm a CSfag (graduated years ago) so I do know vague shit about math like, integrals are continuous sums; that sigma thingy is a discrete sum; if I want to calculate the probability that x is higher than something I need to calculate the area of some segment in the normal distribution (cdf IIRC) so it's a limited integral, i.e. integral from something to something.

But obviously if you make me prove this shit or tell you about theorems I'd spill my spaghetti and start blowing smoke out of my ears and overheat so I still considered myself a noob. I recall when I tried to prove some simple stuff in OP's book I was humbled by how difficult proving this simple stuff is. Much more difficult than plug and chugging (most) CS or Engineer level math and logic, that's for sure. I also wish I knew more about category theory, I see it all the time when I read about functional programming and algebra.

Anonymous at Thu, 21 Mar 2024 01:26:36 UTC No. 16088942

>>16088828
Kek should've gone with Dr. Shlomo instead

Anonymous at Thu, 21 Mar 2024 01:54:35 UTC No. 16088960

>>16088883
I went straight into baby rudin after this book, I wouldn't recommed doing this. I wish I had read how to properly do proof contructions first, some of the exercises where a bit too much, but the chapters are very readable and enjoyable. Thus the answer that other anon gave is pretty good I suppose.

Anonymous at Thu, 21 Mar 2024 02:36:09 UTC No. 16088990

>>16088806
he is just pointing out that calling -a “negative a” can be confusing, because if a is a negative number then -a isn’t negative! (if you were not confused by that, then congrats ur smatter than Serge Lang)

Anonymous at Thu, 21 Mar 2024 02:36:35 UTC No. 16088991

mathlet, so take it with a grain of salt, but as far as I can see he has a problem with calling -a "negative a" because if "a" were something like
>-5
that would be a double negative, which would make it positive:
>-a = -(-5)
>-a = 5

I don't understand why he appeals to properties after, that's where he loses me

Anonymous at Thu, 21 Mar 2024 02:42:58 UTC No. 16088992

>>16088991
>Because of the property a + (-a) = 0, we call it the additive inverse of a.
“Property” is just referring to the equation. “Inverse” is like undoing something. So he’s going to call -a “the additive inverse of a” sometimes. Later in the book he will start calling 1/a the multiplicative inverse, and introduce some other things he calls inverse

Anonymous at Thu, 21 Mar 2024 03:56:08 UTC No. 16089039

>>16088991
>why he appeals to properties after
it's the axiom. he's in the middle of describing the axioms for a group or vectorspace.

Anonymous at Thu, 21 Mar 2024 10:03:16 UTC No. 16089278

Calling -a "negative a" is an assumption unless its known that a is positive. If you dont know that a is positive and your being asked to find a but are under the impression that a is negative because your prof called it that youd just end up with a double inverse and get the wrong answer calling it "minus a" is clearer language

Anonymous at Thu, 21 Mar 2024 10:13:44 UTC No. 16089284

Negative numbers do not exist.
If arithmetic operation a-b is less than 0 this means impossible operation overflow into imaginary space

Anonymous at Thu, 21 Mar 2024 10:14:32 UTC No. 16089285

>>16088990
> calling -a “negative a” can be confusing
I don't think it has ever confused anyone. Lang isn't smart for being autistically pedantic.

Anonymous at Thu, 21 Mar 2024 16:32:18 UTC No. 16089591

>>16089285
anyone writing a math textbook is going to be autistically pedantic

Anonymous at Thu, 21 Mar 2024 19:37:27 UTC No. 16089828

>>16088806
When I was a kid I would've just called it negative negative a honestly.

Anonymous at Thu, 21 Mar 2024 19:40:09 UTC No. 16089831

>>16088806
retarded mathematics tries to make negative numbers a thing.

Anonymous at Thu, 21 Mar 2024 19:42:06 UTC No. 16089836

>>16089831
you aren't a serious person.

Anonymous at Thu, 21 Mar 2024 20:11:28 UTC No. 16089871

>>16088806
i love the way he writes

Anonymous at Thu, 21 Mar 2024 20:35:43 UTC No. 16089920

>>16089871
Straightforward and specific?