Umm… I understand what you’re saying, but the term ‘indefinite number’ means something else I believe… it’s generally used to refer to a numeric variable in algebra. (like ‘x’.) By that standard, 0 is a definite number and an integer.
It is an ‘unnatural’ number, in that natural numbers are the ones that you can generally use to point to. (You can also point to positive rationals in some cases, like 3 and a half apples, where 3 1/2 is not a natural number, but that’s another issue.) 0 is unnatural, as is -3: you can’t point to negative 3 coconuts either. But they’re still definite in terms of mathematics, where concepts are more important than physical objects anyway.
Very likely getting my terms confused. I remembered this thread about whether zero was a finite integer or not.
math?!? ‘Piffle,’ say I! It’s all about physics, where zero is a non-finite, or indefinite, interval or value.
Sure I can! Why this one time, I met five coconuts who were soooo negative about everything
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I can, if we are dealing with something directional; tho, I suppose that’s merely a convention describing (e.g.) west as (-east). I guess it all boils down to the vocabulary you are using based on how you play with numbers. So when mathematicians and physicists start talking about numbers, all hell breaks loose. And og forbid if you invite any chemists or even biologists!
I think you missed the point of what he was saying. You can’t ‘plug 0’ into f(x) at all. It doesn’t matter what the limit is. The value of this function at 0 is undefined.
Mangetout
Yep - good catch there. I was wrong.
I was speaking informally with lots of incorrect “conclusions” thrown in. However, what I meant to say at that point was “since zero divided by any number equals zero then 0/0 must be zero”. (Which, I know is an incorrect conclusion).
Limits in the plane are a bit hairier than limits on the real number line. On the real number line, you can only talk about limits coming from the left or right. In order for the “total” limit to exist, all you need is for the left hand and right hand limits to agree.
In the plane, however, the limit has much stronger requirements. You can approach the limit from the left, right, up, down, at an angle, along some “curvy” path, (or even “worse”, like a nowhere differentiable path).
In 1), if we approach (0,0) along the parabola x=y[sup]2[/sup], the limit will be 1. Along other paths, it will be infinity, as you mentioned. Along still other paths, it could be any number you like. So the limit does not exist (not even in the sense of going off to infinity).
Similarly, in 3), approaching (0,0) along the parabola x=y[sup]2[/sup], the limit is again 1. Along other paths, you could have an infinite limit, or any real number you like, as before. This limit does not exist in any sense, either.
