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Comments:
<0> I see - so it has a stronger historical presence than - well - now
<1> _llll_: my humble opinion, it's all just paraphrasing dedekind's "god created the integers"
<0> I'm on the outside for formal study looking in, but I do want in, and I do acknowledge it requires well, a no nonsense approach
<2> _llll_ what do you suggest?
<3> personally i like category theory, but lambda calculus can also be used
<3> or even conway's game of life
<4> _llll_, i think what set theory had to say it already said,theres not that much more to say bout it
<0> llll - as to the why here, oh, just to learn more I suppose, but I WILL keep it to math related (difficult task for me heh, just saying it's a difficult task already veered off course)
<3> i think there's a lot ot be said for a more computing-based approach
<2> yeah, computation in other words...
<2> agreed, but hard to translate between one and the other...
<1> _llll_: i'd still go with set theory. it's the most bang for the least axioms
<2> your take of axiom of choice?
<4> Landrew, either that or get f*ckin banned lol
<3> there is still set theory being done, large cardinals and the like, but it's not so great for foundations imo
<1> _llll_: it's a bit tomayto tomahto. they are all equivalent.
<4> _llll_, those are very very hard problems,actually more like research
<0> so, set theory is 'a tool' in the toolbox
<4> Landrew, no offence,but really these are the rules here
<0> spx2 - oh, I know
<0> and I can respect that when reminded if I veer
<0> I see the chan when lurking, lots of problem solving in here
<0> and usually ? really ? the investment people have made into the symbiology, syntax and grammar needed to solve or approach problems as they are in here ?
<4> Landrew, like ...if you dont understand them,someone here will make sure you will,and if you do not you can go on the "other side" with fruitbag and all other whizkids here lol
<0> I get that - I mean, I get that it's a no nonsense chan
<0> spx2 - oh, I've learned
<3> Landrew (and everyone else): you can go to #not-math for off-topic stuff
<0> I've been removed from here in the past... Just saying on the rules - CLEAR>
<3> that;s what it's there for
<0> yep
<0> what is a more modern theory over set theory ?
<0> I saw reference to 'lambda calculus'
<4> _llll_, sorry i forgot to ask, can i pm you ?
<0> I know one thing, I had Wolfram as my startup page for about 6 months, and my god, sooooo many sub divisions one can study and seek expertise, real eye opener for me
<5> in which intervall can exp(x) be approximated to 10^-3 with the taylor polynom P(x) = 1+x+x^2/2
<5> i'm not sure if my english is correct
<1> Biggus****us: you want to look at the error, which is the rest of the expansion. or use the taylor theorem.
<5> with approximate to 10^-3 i mean that the 3 digits after the points are identical with e^x
<1> Biggus****us: do you know the exact statement of the taylor theorem?
<5> yes
<5> http://upload.wikimedia.org/math/e/0/e/e0eae846ed9020ced087b7d18302a10a.png
<5> u mean that formul
<5> +a
<1> Biggus****us: there is more than that. there is also a way to express the error
<5> ya
<5> lagrage
<5> lagrange
<1> Biggus****us: okay, so that's one starting pint.
<1> Biggus****us: okay, so that's one starting point.
<5> wait
<5> R(x) = D(f,n+1)(c)/(n+1)!(x-a)^(n+1)
<5> D means differentiated
<1> Biggus****us: right. now if your question is to find out exactly the interval, then you are solving for e^x-(your approx)=10^-3
<5> heh
<5> lol
<1> Biggus****us: but if you want a safe interval, you can derive it using that formula
<5> that would be the easy way
<1> Biggus****us: in a practical case you usually use that lagrange formula or something similar to find a safe interval.
<1> Biggus****us: it's less a math question than an engineering question
<6> hello, how does one determine the restrictions for the expression (tan x) / (2cos(x) - 1) ?
<6> (in terms of cos x)
<1> linolium: what do you mean by "restrictions"?
<5> TRWBW: in the formula above i have a and c
<5> for a i think 0 'fits'
<5> but what do i choose for c
<5> the same thing as x?
<5> to make it max?
<1> Biggus****us: pretty much. you want to find an interval for c such that the formula doesn't exceed 10^-3. that's the same interval for x.
<7> tits?
<7> oh, fits
<1> Biggus****us: your really get 2 values, one negative and one positive, the interval is between them
<8> I wonder if |xy/(x^2+y^2)| <= 1, I can't find any numbers x or y that will get a result larger than 1. How can I prove or disprove it?
<5> i end up with exp(x)/4!*x^4 <= 10^(-3)
<5> how can i solve that
<1> Biggus****us: in closed form? i don't think you can. i'd solve it one a computer. ;)
<1> Biggus****us: btw, didn't your approx stop at x^2? maybe that should be a 3! etc.
<5> ah yes
<5> it starts at 0
<1> Biggus****us: just go by the formula and reason it out. if you are doing it this way, you are looking for an approximate interval, so you can approximate a bit in the solution, make it something easier to solve.
<9> Haha what a humble name
<10> it's from monty python
<9> ah yes
<5> thanks TRWBW
<1> Biggus****us: np. say hello to Incontinentia for me
<4> Biggus****us, use Lambert W function
<5> will do
<5> :)
<5> spx2: my cas told me that too
<5> but i don't know it
<4> "my cas" ?
<5> Computer Algebra System
<5> maple
<1> spx2: yeah, but what are you going to do with productlog except evaluate it on a computer? it's not really a "closed form" in my book.
<4> TRWBW, i know
<4> heh
<4> maybe he was searching for an exact answer
<3> you could say the same about exp(x), or a^b for non-integer b
<4> i just thought i would give some theoretical(because it remains at that level) insight
<3> even "pi" you have to evaluate on a computer
<6> 3.14159265358979
<1> _llll_: they have properties you can use to work with. you can write something in terms of them and do more operations and simplify. but yes, it's just a matter of opinion.
<3> and the lambertW doesnt? :)
<1> _llll_: that's a bit of a stretch.
<3> not sure i see why
<1> _llll_: maybe i just don't know the. lw(a+b)? lw(a*b)? lw(a)*lw(b)?
<4> _llll_, for practical issues lambertW is useless
<3> no dout wikipedia can tell us how lw works. my point is that "closed form" is not an absolute thing. could talk about galois theory here
<1> _llll_: i think everyone is admitting it. but there is a practical distinction. and it's a matter of opinion. and my opinion, lw isn't a useful closed form.
<9> is it possible to factor: b-3(sqrt(b))-10? I can't figure it out, so I was just gonna use another method
<1> saxofoner: if a=sqrt(b) that's a^2-3a-10. does that help?
<9> where'd a come from?
<9> or did you substitute?
<1> saxofoner: substitute
<9> ah
<9> yes
<1> saxofoner: i was making it clear that you can use the same technique as for any quadradic
<1> saxofoner: i thought that would be more helpful than just saing (sqrt(b)-5)(sqrt(b)+2)
<9> oh thanks. I hadn't gotten that. I was thinking okay. x=b. no wait. that doesn't help... but thanks, you hit the nail on the head
<1> saxofoner: np
<11> hi, how can i solve for constant k in this system of equations? "2 = kx; 4 = k(x-1);"
<11> note that x nor k are given
<11> and k is constant
<12> substitute the first into the second
<1> whats_in_a_name: do a=kx and b=k. then its a=2 a-b=4.
<1> whats_in_a_name: or what Dacicus said
<8> does anyone know if |xy/(x^2+y^2)| can be larger than 1?
<1> norton: try (x-y)^2>=0 and expand out
<0> this is a silly question, but is the reason we have area of a triangle (1/2)bh is because a square is two triangles ?
<0> where square is area = bh
<13> square? :)
<1> Landrew: yes, you can cut it up and form a square from it.
<0> I know that's silly, but I never 'thought' about it
<1> Landrew: that is from 2 of them.
<0> until recently
<0> ok. again, that's 'pretty basic'
<9> i did that on my sat
<9> haha
<3> except not every triangle is half a square
<9> I couldn't remember a tris area, so I drew a square and chopped the triangle out of it
<0> right
<0> llll- yes
<12> some are half rectangles
<9> it was a right triangle
<9> yes
<9> that's true
<9> only for right tris
<3> but it's the right idea
<12> and some are half quadrilaterals of other types
<0> one other question from geometry, if you put a triangle inside a circle, is it that the area outside the triangle, but inside the circle = area inside the triangle ?
<14> Triangles are half-parallelograms, if you want both halves to be triangles.
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