So My Calc teacher said..

[Anonymous No.3704256]

We're going over limits already, and my teacher said that when you substitute 0 in for x, and you end up with 0/0, you have to multiply by the conjugate to get rid of the 0's. I argued that 0/0 = 1, because that's just how I saw it and the wholle class raged at me for asking a question they didn't understand. I don't get why it wouldn't be 1, and my teacher couldn't explain. Help?
Pic very related, it's the equation.

[Anonymous No.3704267]

it is impossible to divide by zero you noob

[time for a haiku No.3704265]

Divide by zero
Operation undefined
On real field

[Anonymous No.3704280]

The answer would be infinity cause you could divide it by any number and still get the correct andwer

[Anonymous No.3704284]

0/0 = 7
0/0 = 0
0/0 = Niggerjew

Depending on the function that produces 0/0, it can equal your fungally infected toe.

[Anonymous No.3704293]

2 = (2x0)/0 (since 0/0 is 1 this is true)

2x0= 0

so 2 = 0/0

so 2 =1 ..... that's why 0/0 can't be 1

[Anonymous No.3704302]

>>3704284


OP think about it logically.

you have 1, ration 2 = 1/2
you have 3, ration 3 = 1
you have 0, ration 0 = ???

If you do not define the amount you ration then the amount rationed is undefined.

[Anonymous No.3704303]

Any number multiplied by 0 is 0
Any number divided by 0 is undefined
Any number divided by itself is 1

We can't prioritize any specific rule, so 0/0 means there's something there, but you need to do some extra steps to find it out.

[Anonymous No.3704306]

expand the denominator or use l'hopitals rule.

If you expand the denominator you get x/(x + x^2)
since the denominator has a higher degree x term it goes to 0.

[Anonymous No.3704310]

He tried explaining it like
3*5=15
5*3=15
30*.5=15
So
If I was saying 0/0=1
then 0*1=0
I don't understand why we even teach zero as an amount on graphs and all that, if it never works on the equations.

[sage No.3704311]

>>3704306

Implying they have gotten to l'hopitals in his calc class already

[Anonymous No.3704327]

Consider the functions x/x, 2x/x and x^2/x.
They all are of the form 0/0 while taking limits.

But x/x approaches 1.
2x/x approaches 2.
and x^2/x approaches 0.

[Anonymous No.3704328]

>>3704303
What would those extra steps be?
Btw, thanks for the help guys.

[Anonymous No.3704356]

It's fine to cancel the x's in your picture like that, if that's your question.

x/x = 1 for all x except 0. But since it's a limit, we don't actually care what happens at x = 0.

But normally 0/0 can get you anything. For instance lim x-> 0 sin(x)/x = 1

[Anonymous No.3704360]

the problem with division by 0 is that it could justifiably be any value between negative infinity and possitive infinity.

To understand why, look at the graph of

y=1/x

http://www.wolframalpha.com/input/?i=y%3D1%2Fx

The idea is to find out what happens at x=0, or y=1/0

If we approach 0 from the negative side, by assigning negative values for x that get closer and closer to 0 then we'll end up with a strong argument saying that 1/0 is equal to negative infinity.

Similarly if we do the same thing with positive values we'll get the argument that 1/0 is equal to positive infinity.

The fact that they can't both be right leaves us having to accept that 0/0 is simply undefined. Though using a Reimann Sphere we can have a special case where negative and positive infinity are equal.

Either way, in calculus you're not just dealing with 1/0 you're dealing with 0/0. To better understand why one need only look at zeno's paradoxes. For example, a hunter shoots an arrow at a deer and he wants to know how fast the arrow is traveling at a certain point. He can figure out the average by calculating the distance and how long the whole trip took. Though if he wants to know a specific time period then he'll have to do distance/time with ever smaller intervals of time and distance. Suppose you were to stop time to examine the arrow in mid flight. Now the arrow is not moving, so it's not traveling any distance over any span of time. Though it still has a speed, if you try to calculate it without calculus you're effectively doing 0/0. It's not a problem with the values, just a problem with the approach, because clearly the speed of the arrow is not 1.

[Anonymous No.3704366]

lim x->0 x/x(x+1)

1/(x+1)

as x->0

1/(x+1) -> 1

seems simple enough to me. 1+0 = 1. 1/1 = 1.

[Anonymous No.3704382]

>>3704366

http://www.wolframalpha.com/input/?i=lim+x-%3E0+x%2F%28x%28x%2B1%29%29

Link related, wolfram alpha agrees with me.

[Anonymous No.3704385]

>>3704310

Your teacher is an idiot, however 0 has a lot of special properties that you can't understand with a classical understanding of mathematics. If you're not a math major then you should just deal with it because you'll never amount to anything anyways, if you however do need to truly understand mathematics then I recommend you ditch your professor and teach yourself out of books, also read up some math history it will help you tell why shit happened and what are actually mathematically rigorous processes vs what are just arbitrary conventions used so that every understands each other (like pemdas).

[Anonymous No.3704492]

The limit never reaches zero... so you aren't really dividing by zero, you're dividing by a number extremely close to zero. I don't see a problem.

[TenchiMuyo1984 No.3705852]

lim x->0 { x/[x(x+1)] } = [0/0]

L'Hospital lim x->0 { f'(x) / g'(x) }

f(x) = x => f'(x) = 1
g(x) = x² +x => g'(x) = 2x +1

lim x->0 { 1/(2x+1) } = 1/1 = 1

[Anonymous No.3705956]

>>3704256
Don't listen to the division by zero nazis, zero divided by zero is a special case.

Division is simply the inverse of multiplication, so what we're looking for is something satisfying x*0 = 0 (0/0 = x => 0 = 0*x) and of course, anything satisfies this. The reason 0/0 is undefined (unlike other cases of division by zero) is simply because its undefinable as a function, if we define it simply as a relation then any real number is fine as the solution to 0/0. People like functions more than relations is all (and the arithmetic division is typically taken to be one, but it really need not be, depending on purpose...)

Of course your teacher wants division as a function, and as a function its undefined at 0. There's nothing mystical about being undefined either, like the nazis will have you believe. Division isn't defined on letters either, or on cats. It just so happens that 0 is mildly interesting in that its the only real number for which division is not defined. You don't put cars into refrigerators, you don't put zero into division.

[Anonymous No.3705967]

This is why I only use multiplication and addition on whole numbers for my math.

[Anonymous No.3706030]

>>3705956
Not quite how I'd have worded it, but that's pretty much it. We define the arithmetic functions, we could define them however we pleased. We constructed addition such that 1+1 = 2, we constructed division in such a way that there was no 'sensible' single answer when we divide by zero, so we just didn't define it at 0, because we wanted some flexibility when it comes to division by zero to work to the context of the problem, so that we can produce the answer that's sensible at the time by further analysis, rather than being stuck with something ridiculous.