You are not allowed to use L'Hôpital's Rule

practically every us school makes one use l'hopital without proving it (or at least rigorously proving it)

>only asymptotic analysis is allowed
I'm OK with this

I believe two things.

1) No math education should allow a student to use a method before it is rigorously proven in the classroom or perhaps as an assignment. This is lazy. The reason L'Hopital's rule is interesting is that it is one of the first analytic rules for limits that we discovered. You have to remember that the first things we fleshed out when studying limits were the algebraic properties of limits. Things like doing clever substitution, multiplying the conjugate, doing a clever division, etc. Those are algebraic methods. But if you do that you start realizing how limited is algebra when dealing with limits and that is how you genuinely get students interested in going beyond algebra to find the true methods of analysis to be able to have a better toolkit. That is how you get L'hopital's rule and the method of Taylor expansion in limits. That is how you get students to appreciate the power of L'hopital's. That is how you make a clear distinction between algebra vs analysis to new students.

2) That before any serious testing (midterms of finals), the class should have already proven all the modern methods so that when it comes to an actual test the student does not feel limited. And I say this because one thing is motivating mathematics, and another thing is actually testing your mathematical skills. When motivating, less is more, because the less you know the more focused your brain is on the few basic techniques and that is how you can truly appreciate a theorem. But when it comes to being tested, you should have complete freedom of how you wish to approach an advanced problem because that is the essence of mathematics. Freedom.

Imagine the shitstorm you could cause by doing this. I wish I was smart enough to think to pull that one just for the fallout.

>tfw you just use squeeze's theorem instead

Never was taught it, never needed it. As a result, i consider many problems you cuckies struggle with as trivial.

I've got something you can squeeze bitch

1+1=2
Teacher trying to explain the proof to 5 years old kids.
Yeah this is a good idea faggot.

Very interesting, the first part. I didn't know that

Why are you talking about kids? This is a university education discussion. Go back to playing with your legos.

>No math education should allow a student to use a method before it is rigorously proven in the classroom or perhaps as an assignment.
So we shouldn't teach kids to count until they can do proofs?

"Proofs before applications" is a perverted fetish. For the most part, rigorous proofs of the validity of useful mathematical techniques were developed well after practical applications, because they're harder and because a much, much smaller number of people has an interest in them, when a cadre of obnoxious, wrongheaded rigor-fetishists hasn't occupied credential-granting institutions and arbitrarily made a hurdle of them rather than a side track.

For that matter, what constitutes a "rigorous proof" is a matter of taste. People weren't wrong about calculus working for the couple hundred years they used it without any proof accepted as rigorous that it was "valid".

Thinking that math is about rigor is a deep form of confusion about what math is. Math isn't about truth, but about abstract structure. If a method gives consistent results, then it represents a structure. Our interpretation of what that structure truly is, in relation to other abstract structures, is less interesting or important than how it relates to real-world phenomena.

Please, I do not consider anything below university a math education. School is general education.

I am talking about a real math class given in university. In particular a Calc I class which is where you typically see limits.

They didn't like me using complex exponentials for proving/simplifying trig identities

>a Calc I class which is where you typically see limits
That's a perfect example. Starting to teach calculus by teaching limits is idiotic.

The only reason you'd do so is this "proofs first" attitude, when calculus was invented by thinking in terms of infinitesimals and limits as we know them weren't invented until a century and a half of calculus being a central tool of math and science.

You don't need limits for calculus. You don't need limits to teach it, you don't need limits to use it, you don't even need limits to make it rigorous (the infinitesimal model was also formulated rigorously, though this has largely been ignored by the cadre of unpleasant third-rate fanboys who have taken over mathematical education).

What if it's just a 2-year college?

avoids things like these happening

>Muh proofs

I hate mathfags like you who worship proofs as the most important thing when is just a lie.

Mathematicians never advanced maths by your oh so rigorous proofs. They actually just tried stuff, made a mess and then obscured all the work into a "formal proof" so they can say "oh well its obvious just see my proof :^)" The initial intuition and process of developing the idea is better to teach a concept

Okay, I dislike how people are railing against proofs, the cornerstone of mathematics. First of all, I am so sorry you failed your intro to proofs class. I can't say I can relate, but at least I can understand your pain. Second, no. You are all retarded. Mathematics is proofs. There is literally no reason to undermine proofs in modern mathematics. Today we are at such a high level of abstraction that is ridiculously easy to follow your "intuition" into a sea of contradictions. This is because math is more now than "xD lets prove these triangles are congruent" or "xD lets find the slope of this function". We are in the real shit now, and rigor is everything. No one will listen to your claim unless you have a proof. There are too many examples in post 19th century of intuition being retardedly wrong and holding mathematics back in general.

And even in ancient mathematics, intuition was yielding retarded results. I read in an old number theory textbook that back in the old days people through that there always was a unique perfect number inbetween two powers of 10. This is because the first perfect number was 6, then 28, then 496 and finally 8128. So of course our intuitions went wild and people tried to find the perfect number in the 10000s but because of lack of computational power they couldn't. Then fun fact, the next perfect is number is fucking 33550336. So much for "xD lets just try something!".

Intuition is mostly cancer nowadays. Proofs are all that matters when it comes to real math, and intuition should be left for minor explorations by real mathematicians who know how to write solid proofs and want to see what could be beyond. Learn to math.

>reddit mannerisms
>reddit spacing
>xD
>"I read an old number theory book"
>"real math"
>"real mathematicians"
Autism at its finest

>using the hospital rule to calculate [math]\lim_{x\rightarrow0} \frac{\sin x}{x} = 1[/math] but you also used the said limit in your proof that [math]D\sin = \cos[/math]

>>reddit mannerisms
I am sorry, I have not been in reddit nearly as much as you to recognize their mannerisms.
>>reddit spacing
This meme has to die. I separated my thoughts into three paragraphs because my thoughts were separated into three points. Reddit spacing used to be when someone does a line break between every sentence. But as always, you redditfags with your memes take everything to the retarded extreme.
>>xD
I put the xD between quotes, as in quoting you, because I know the 3 retards I was quoting were insufferable redditfags.

i like this because both are equivalent statements

where do you teach?

>reddit! reddit! reddit!
>muh autism
if you're going to try to disagree with him at least say something intelligent. also, i don't think you know what reddit spacing is.

Why respond with intelligence when nothing intelligent was originally said?