Why are mathematicians so autistic?

Wrong

Both of these sound entirely reasonable, OP. Both are excellent ways to arrive at horribly wrong results without noticing.

Switching to a dummy variable is important, you need to show you know how to do it for when you come across those problems in your job.

The only reason you didnt have to is because the prof intentionally made it easy to solve so that youd show the dummy variable and not be bogged down in calculation.

x/0 doesnt equal infinity. Not your prof fault youre a brainlet.

In the limit of some c / x as x -> +0, c/x does equal infinity

Yes. But that is not the stated question. So why did you bring up irrelevant trivia?

That's clearly what OP meant when he said divergent behavior

Then perhaps he should have written that on the test.

That's the point

What about the case c = 0? Or, more generally, when the numerator is a function which goes to 0 as well?
There is nothing wrong by writing, for example,
[math] \lim_{x \to 0} \frac{\overset{\to 1}{e^x}}{\underset{\to 0^+}{x}} = + \infty [/math].
Making some comments indicating why the limit is indeed [math]+ \infty[/math] is ok but writing something like [math] \frac{1}{0} =
+ \infty[/math] is just wrong.

Indeed. In mathematics it is generally required to write things that are true, not just things that are vaguely reminiscent of something that is true.

Ok, the example had some faults...
[math] \lim_{x \to 0^+} \frac{\overbrace{e^x}^{\to 1}}{\underbrace{x}_{\to 0^+}} = + \infty [/math]
should be better (hopefully)

If you didnt make it explicit that you were working over the extended reals then clearly x/0 is wrong.

integrating over dependent limits is not defined

LMAO saying 2+2=5 is WRONG. and you are mad because your professor deducted points for you being wrong

We judge ourselves by our intentions, but other people judge us by our actions. Even if what you are saying is reasonable (it isn't, even in engineering, write what you mean it's literally like five extra characters, only brain let engineering profs would let that slide) how would the Prof be able to tell the difference between some brainlet who thinks x/0 literally equals infinity, and you, if you two write the exact same thing?

Proofing is as old as math. Even though Euclid the elements were flawed, it was still seen necessary even back then to have a systematic and self consistent approach.

All "the best" mathematicians might indeed have had good intuition, but they made sure their ideas were sound.

You can't do mathematics without good intuition and you can't write mathematics without good rigor. No surprise here.

As an amateur who dabbled in both fields I was taken way more seriously in maths for the simple reason that so long as my proof was rigorous not even the Lucasian Professor of Mathematics at Cambridge University could argue with it, whereas my my engineering ideas were just endlessly trashed no matter how much maths I gave to back it up. So now I don't bother trying to discuss anything with engineers I just build it and if it works they can suck a fat one.

AAAAAAAAAAAAAAAAAAAAAAHAHAHAHHAAHHAAHAHAHAHHAHAAHHAHAHAHAHAHAHAA
SO WAIT.
YOU BE SAYIN'
>INEXACTLY CALCULATES SOMETHING BASED ON "INTUITION"
YOU BE SAAAAAYIN'
>DOESN'T ACKNOWLEDGE AXIOMS BUILT ON PURE LOGIC
YOU BE SAAAAAAAAAAAYIN'
>DABBLES IN PROBABILITY THEOREMS WITHOUT STABLE PARALLEL MARKERS IN PROOFED ALGORITHMS
WE
>DOESN'T BOTHER USING DUMMY VARIABLES
WUZ
>LOSES POINTS
WE WUZ
>COMPARES MATHEMATICS TO ENGINEERING
MAAAAATHEMATICIANS 'N' SHIEEEEEEEEEEEEEEET
>LOSES POINTS

Math is the programming language of the universe, you almost have to be autistic to truly immerse yourself in it.

If it's lim_{a->0}(x/a), that would be divergent, because it depends which direction you're coming from. Did it specify direction?

git gud

You're going to be an engineer so you don't need to have that much rigor. But your math teacher isn't just teaching engineers, he's also teaching future physicians and mathematicians, and they can't afford making that kind of mistake.

>go to Britain
>try to drive on the right side of the road
What's the problem officer?

Why the homophobia?

I don't get it.

It's all one big gay wheel user

Some were intuitive others focused on building knowledge axiomatically. Both types of minds are important.

>physicians

answer is simple, mathematics are as hard and inside the lines as you can get in what we know as reality... even physics can't change the fact that 1+1=2, your pleb neighbor even uses that as a pop-culture reference from time to time -

so yeah, i can understand a hardline mathematics professor not taking a joke when you blend mathematics and the real world

furthermore, the whole reason he probably took a dead-end career in academia mathematics was specifically not to deal with that type of question

I actually found the majority of my fellow math majors to be pretty normal. We had a fair amount of girls (math education), and some spergs, but not as muc as engineering, especially ECE. Mechanical engineering had a fair amount of bros in it and chemical engineering had a fair amount of women in it. Physics had almost no women in it except for one or two ugly ones. This was true at Virginia Tech.

math is a conscious construct, therefore, it will always have trouble when explaining the universe (a unknown construct)

let me preface this by, i love you guys, keep growing, but hesus cristo - never forget that relativity was when we realized we know nothing... look up the speed of light, and it's tests in reality. what is it? how accurate is it?

it's why einstein died in a state of extreme annoyed

Annoyed that he couldn't steal ideas from the patent office

To lazy for a dummy variable? Literally just stick a ' or something onto the end Jesus
Also x/0 = [math]\infty[/math] is a literally, objectively wrong statment
He's not being pedantic, you were just wrong
I'm a physicist, and there's a time and a place where 'results' are fine, and a time where 'pedantry' is required. A maths exam is one of those times where pedantry is required
Sorry to be a jerk OP

Marking x/0 = infinity wrong is just pedantry, but having the same variable inside the integrand as in the limits of integration is indefensibly wrong.

The world is filled with pathological structures and systems which make them hard to predict or analyze with models that makes too many assumptions. So what do you do? You make less assumptions. You work with as little axioms as possible. But what are you left with? You have no calculus because nothing is differentiablem no algebra because nothing forms a clear defined space. No analysis because nothing is smooth and continuous. No geomety because nothing is symmetrical. What do you have? Just raw discrete logic. The most basic notions of the truth and what can be extrapolated. Mathematics can be seen as an extension of logic, but for now just see the two separately. The world is complex, and logic alone isnt enough. You need to build on this vlear definitions. But generality has the price of abstraction. Your answer is that the world is autistic, not mathematicians my friend.

The speed of light is exact since it's used to define the meter.

In the real world 1 + 1 = 1 or any other arbitrary value.
Proof: I have two pieces of gum and stick them together.

What op did wasn't a joke. It wasn't correct and he deserves to lose points.

>In which wheel?
Stop posting that in every thread related to division by zero, nobody is impressed you read the wikipedia article on wheel theory.

WTF class is this "elective" in your engineering major? You mean Calc 2?? That's not an elective. You're supposed to be demonstrating sensitivity to the math.

The professors who teach engineering students are always those with the crappiest research. They're butthurt about being inferior to everyone else in their department and take it out on their students.

I can relate to this, user. Cause I feel the same vibe from my professor

Here, have a rare Wildberger

you were wrong in both cases, period. why do you think you should be getting points for wrong answers ?

>Stop posting that in every thread related to division by zero, nobody is impressed you read the wikipedia article on wheel theory.
How else is anyone supposed to interpret the division?

9=/=1
0.9=/=1

ceteris paribus

0.99999999...=/=1
Q.E.D.

>taking calc 2
>don't bother to research the professors be because it's calc 2
>my professor is an engineer with no title in math
>apparently, the math department has "support staff" that sometimes helps with the basic classes
>whatever it's calc 2
>get 100% in the first test even though I know I made some mistakes
>next test I pull out a calculator and do everything with it while writing nonsense in the procedure
>still get 100%
>professor's review week arrives
>write what I did
>the math department doesn't have support staff anymore
I don't know if it was my doing but damn it felt good.

>Expecting adjunct slaves to read every letter

You made a bunch of profesors lives harder becuase you felt the need to report an aid for giving you an easy a in a meme class.

Easy As are the reason you have students in ODE who can't do u-substitution.