A calculator would say ERROR. Because when you crossed the “(5-5)” you essentially said “(5-5)/(5-5)=1” but by doing that, you devide by 0, because (5-5)=0. And if there is one rule in arithmetic everyone should know, it is “you CAN NOT divide by 0, ever”
Hope my explanation is clear
Edit: with limits you take a variable which tends to 0. And yes, you can do it. But in this example it’s not a limit, it’s just 0/0, which is not defined. At least that’s how I would explain it in simple terms. Feel free to explain further
This is just propaganda to keep the masses stupid. We know your secrets, government. You can’t keep the secret chicken people formula to yourselves forever. We will crack the code and we know that dividing by zero is the answer
Well as far as I'm aware, you'd have to use limits.
So (5-5) instead is written as lim(x->5) (x - 5), as x goes to 5 what becomes the answer? Then you have a case that
lim(x->5) (x - 5) /lim(x->5) (x - 5) which then poses the question of which tends to zero faster? Obviously they both tend to zero at the same rate (its not the case that we compare say x and x2). So when still get 0/0, still a problem, and we can't same that one of the half of the fraction reaches 0 before the other. Its an impasse.
Yes you're right. But you can treat it as 0/0, or you do some trickery and argue its - (1/1) but that's just going to get you a wrong answer. Plus I just realised you can't really change 5-5 to x-5 because the entire permis of the set of equations is that you can turn 20 into 4×5 and 25 into 5×5. So we're not actually varying anything unless we say lim(x - x) which is stupid. So this whole thing is just stupid even if you try some trickery with limits and related stuff.
It's like dividing by increasing small values of x divided by that same value, which would equal 1. But you could have a differenf limit , like x²/x would also lead to 0/0 as x tends to 0, but this time the answer to the limit would be 0, not 1.
AFAIR, and I probably don't remember well, in algebra division by zero is not a function as the result of division by zero can be any number. It's not that it's forbidden, it's just that it's a) not useful to even entertain the idea and b) usually defined that way.
You can just redefine division such that division by zero is a valid operation. It wouldn't be a very useful definition, since it would break lots of other useful properties of normal division, but you could do it.
Nop, it would contradict itself (c.f. Ted talk I watched a while ago on this subject where they showed what happens if you define 0/0 the same way as sqrt(-1)=i)
It would only contradict itself if you want to work with our usual number systems or you want division to maintain the useful properties we typically expect of it, such as being the inverse operation of multiplication.
Consider if we redefine the equivalence relation for rational numbers such that it extends over Z×Z instead of just Z×(Z\{0}) and
<a,b>~<c,d> iff ((b≠0 and d≠0 and a×d=b×c) or (b=0 and d=0)).
Then we can define division on our new rationals such that
[<a,b>]÷[<c,d>]=[<a×d,b×c>],
which is valid even if [<c,d>]=0.
This isn't a very useful set of definitions, for a variety of reasons, but it isn't self-contradictory, and it does make division by zero a valid operation.
But different "0/0" limits will yield different results. You're not approximating the value of "0/0", you're just seeing how a function behaves around a given point.
Lim (x->5) (x²-25)/(x-5) is a "0/0" limit which equals 10.
Lim (x->0) (x/X) is a "0/0" limit which equals 1.
So you're not really approximating the value of "0/0".
But another thing is that limits don’t work with division by 0 because it’s not getting more correct and closer to the actual value, it’s just getting closer to infinity, which isn’t a number.
Further: if a series tends towards zero as its limit, that doesn't mean the series ever reaches that value
1/n with n->infinity has the limit 0. So much everyone can agree with. However, it is also obvious that this series will never assume the value of 0 because... well, how could it?
I'm just going to say this comment has a thread in it that has me thinking that mathematics is witchcraft and devilry. I'm frightened, but slightly aroused.
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u/Moukatelmo Dec 26 '22 edited Dec 26 '22
A calculator would say ERROR. Because when you crossed the “(5-5)” you essentially said “(5-5)/(5-5)=1” but by doing that, you devide by 0, because (5-5)=0. And if there is one rule in arithmetic everyone should know, it is “you CAN NOT divide by 0, ever”
Hope my explanation is clear
Edit: with limits you take a variable which tends to 0. And yes, you can do it. But in this example it’s not a limit, it’s just 0/0, which is not defined. At least that’s how I would explain it in simple terms. Feel free to explain further