What

what

Thats why you dont divide by zero, fucks shit up

lines 1-4 make sense, but on the 5th line, it becomes nonsense.

unless it is a limit

On the 5th line, because (a-b) is equivalent to (a-a) and 0, its division from both sides of the equation is invalid.

differentiation is literally dividing zero by zero.

the 4th line doesnt make sense, everything else is good

can someone explain 4th line ? i dont understand it

nvm it all makes sense, wtf

no

This is literally not true. You are dividing values that are really, really close to 0.

If you were literally dividing by zero then then derivatives wouldn't even exist as for all f and all x defined for f, f(x + h) - f(x) = 0

as h is just zero, as you claim it to be.

The fact that this does not happens immediately points out that the values are very distinct from zero

>the 4th line doesnt make sense, everything else is good
you dont make sense and are a retard, eveything else is good

protip: if you unironically cant debunk that t-shirt, you need to fuck off back to /pol/.

being this mad

>the state of neo-Veeky Forums

you look at the limit of a fraction p(dx)/q(dx) where both p(dx) and q(dx) go to 0 as dx goes to zero.
Very clearly we divide 0 by 0 here.

both of you are autists

>goes
>TENDS
you're literally contradicting yourself here

If a=b then (a-b) = 0
qed

lets trace back the actual conversation so your fucktarded mind may be able to comprehend.

If you trace back who responded to what, you'll see that the conversation went like this:
> Thats why you dont divide by zero, fucks shit up
to which some user replied
> unless it is a limit
to which I replied
> differentiation is literally dividing zero by zero

so here's a multiple-choice popquiz for you, fucktard. Do you think that
a) your fucktarded and I literally meant dividing the natural number 0 by itself or do you think that
b) your fucktarded and I meant that differentiation is 0/0 as a *limit*, or do you think that
c) your fucktarded, I fucked your mother last night and she told me your sister got aids from you?

Choose now, and choose wisely.

Not that user, but I want to believe c, if that helps

>use the word literally
>don't mean literally
Don't be a nigger.

There are two really common ways people do this and once you know them these are really easy to point out:

Either they fuck around with algebra and then end up dividing both sides by 0 (in this case a-b) and the rest becomes garbage.

Or, they'll take the square root of a square and fail to account for the fact that that results in the absolute value.

There is no such thing as 'limit'. Unless you're talking about the categorical concept.

Norman wouldn't like the categorical notion of limit, either. The direct limit generalises the usual notion of limit, for example.

There is no differentiation here :-|

I love summer

Who said there was

DON'T DIVIDE BY ZERO !!!!!!!!!!!
RRRRRRRRRRRRREEEEEEEEEEEEEEE !!!!!!!!!

If a=b then (a-b) = 0
line 5 is 0=0
line 6 is wrong, not because you divide by zero, but because you don't know how to multiply.

Line four is bullshit. You can't multiply by 2 on one side, and not do the same on the other and have it be equal.

Differentials are not numbers you idiot

You can't right cancel, nobody ever said a,b live in a domain.

You don't multiply by 2 retard
You're subtracting by 2ab on both sides

You guys think you're smart, but your all retarded

line 5 is 0=0 you can't go to line 6 from there

there's a reason you are told to simplify variables, else it can get messy.

if a=b, then
a^2 = a^2
2a^2 = a^2 + a^2
2a^2 - 2a^2 = a^2 - a^2
2a(a-a) = a(a-a)
The problem becomes obvious.
You could also try using the real method for this kind of equations.
2a^2 - 2a^2 -a^2 +a^2 = 0
0=0

This is a Spivak's first chapter problem. You guys praise that book so much though you can't solve this.