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[MagmaMcFry]

In a strictly mathematical sense, your assignments are totally valid, yet your teachers are stupid. You could check if they would allow you to use s(x), c(x), t(x) instead.

[Another]

The potential for a problem is when you have sin(x), sin(y), sin(2*x), sin(x₂) sin(x²) [ok, last one is extremely unlikely to arise in any practical case] in the same problem.

[Sergarr]

sin(x²) [ok, last one is extremely unlikely to arise in any practical case]

http://en.wikipedia.org/wiki/Fresnel_integral

[Skyrunner]

The potential for a problem is when you have sin(x), sin(y), sin(2*x), sin(x₂) sin(x²) [ok, last one is extremely unlikely to arise in any practical case] in the same problem.

I said that I assigned only and only "sin x" to "s", "cos x" to "c", and so on. So that's a non-problem.

Also, if I use s(x), c(x), t(x), that's even less of a problem.

[Vector]

Enjoy your later courses on metric differential geometry, because you will be using r, s, and t as function names and c as a constant.  And you'll also be using sin, tan, and cos, etc.

The way it works is that letters are taken for different things.  So we like f, g, h as functions until we get more than 3, and then we do f₁, f₂, f₃, etc.  x, y, z are usually unknowns.  And s, r, t, are things you call functions in domains that are more commonly physics based (I think.  Someone should correct me if I'm wrong--but I know that they're taken).  Training to communicate in this way is part of mathematical culture and makes it easy for mathematicians to interpret work at a glance.  You can figure out much faster which kind of math you're reading, and which sorts of tools the author is more or less likely to use.

Similarly, we don't name the variables for our equations words, we name them letters; we've got a convention that a string like "egg" means "e * g * g," even if it would be cuter to solve for "egg" than "x."

So no, it is not incorrect to name your variables whatever you want from a technical perspective.  From the perspective that math is a thing that humans read, however, it is best to listen to your teacher.

[Skyrunner]

But my course isn't metric differential geometry :c

^{_{Also I'm not entirely sure  Geometry and Vectors and Math II tests are what you'd call math >___> but then again I'm very biased against them}}

anyhow: any links to r/s/t as functions? Simply searching for "function t" shows up model rc helicopters, and filtering out repeatedly leaves me with Owen's T-function, a cryptography function that does something.

[Vector]

You're learning Mathematics.  Mathematics is all one piece, a prism learned from different perspectives.

[Skyrunner]

I'd like those two subjects, along with Integration and Statistics a lot more if it wasn't about pulling off brutally freakish feats like solving twenty-five difficult(harder than IB, harder than AP Calc, at least) problems in 50 minutes. :x

I mean, limits and differentiation were the most awesome and intriguing things I've learned of for a while. Soon I'll be able to actually calculate the length of a curve o_O

[Errol]

A short question/is-this-proof-okay, since apparently over uni break I lost what little mathematical skill I had left. Apologies if some terms sound weird, I probably translated them literally from German.

The assignment was to prove that the space X of bounded functions f : [a,b] -> |R with the supremum norm is a Banach space. This means I have to prove that X is complete and normed. The latter property is per definitionem, as the supremum norm is a norm. As for the former property, since all f € X are bounded, any Cauchy sequence formed by their (finite) norms will not 'converge' towards infinity. Also, since |R is a complete space, any Cauchy sequence in |R converges, so any Cauchy sequence of the supremum norms will converge towards one specific limit, y. It is easy to construct a bounded function fy = y whose supremum norm is y. Thus, every Cauchy sequence on X under the supremum norm converges, Q.E.D.

Where's the holes? This feels too simple to be true.

[Vector]

Because there's so many common functions named s, t, r, and c that it's extremely bad practice.

We used S T and R as slack variables when doing the simplex algorithm at school. Never seen it used otherwise, except in bog standard algebra questions instead of any other letter.

It's quite common to have t stand for time and s and r refer to position in terms of time, when one is working with physics and anything that came from it.

[MagmaMcFry]

A short question/is-this-proof-okay, since apparently over uni break I lost what little mathematical skill I had left. Apologies if some terms sound weird, I probably translated them literally from German.

The assignment was to prove that the space X of bounded functions f : [a,b] -> |R with the supremum norm is a Banach space. This means I have to prove that X is complete and normed. The latter property is per definitionem, as the supremum norm is a norm. As for the former property, since all f € X are bounded, any Cauchy sequence formed by their (finite) norms will not 'converge' towards infinity. Also, since |R is a complete space, any Cauchy sequence in |R converges, so any Cauchy sequence of the supremum norms will converge towards one specific limit, y. It is easy to construct a bounded function fy = y whose supremum norm is y. Thus, every Cauchy sequence on X under the supremum norm converges, Q.E.D.

Where's the holes? This feels too simple to be true.

The proof is actually as simple as that, yet you may want to order your thoughts a bit. The only thing you really need to show is that any function sequence (that is a Cauchy sequence under supremum norm) converges pointwise to a bounded function, which is easy to show since |f_m(x)-f_n(x)| is bounded by ||f_m - f_n|| and is therefore uniform.

[Pnx]

Here's one I could us help with.
limit as x approaches + infinity of:
sqrt ( 4x² + 5x ) - 2x

[da_nang]

Here's one I could us help with.
limit as x approaches + infinity of:
sqrt ( 4x² + 5x ) - 2x

Try multiplying with its conjugate (divided by its conjugate so it's equal to one. Name of this operation slips my mind... Extend?).

Spoiler (click to show/hide)

lim_x→∞ sqrt(4x² + 5x) - 2x = lim_x→∞ (4x² + 5x - 4x²)/(sqrt(4x² + 5x) + 2x) = lim_x→∞ 5/(sqrt(4 + 5/x) + 2) = 5/4

[Pnx]

The difference of squares part I get, the second step where you figure out that 5x/(sqrt(4x²+5x)+2) = 5/4 puzzles me though.

[Skyrunner]

Divide both top and bottom by x.
5x becomes 5.
sqrt(4x^2+5x)+2x becomes sqrt(4+5/x)+2.
Since 1/x converges on 0 when x->infinity, the equation equals 5/(sqrt(4)+2)=5/4