Forums → WEPR → 0 is the largest number

One may logically conclude that 0, therefore, is the largest real number.

Non sequitur. The values of X and Y don't alter the value of 0.

-1 < 0 < 1.

0 is the absence of a number.

Its derivative (the slope of the tangent line at that particular point) is y=1/x^2, a graph which, for all rational numbers, has a positive y-value, meaning the graph is constantly increasing in value.

So you're saying based on an asymptote that 0 is the largest number?

One may argue that you are excluding the value x=0, because that cannot be said to have a definitive y-value value at that x-value.. However, look at the derivative, which is 1/x^2. As x approaches 0 in the derivative, y approaches infinity, regardless if you take a positive or negative 0. Therefore, at x=0, the value must be increasing, whatever the corresponding value of y is.

As x approaches 0 in the derivative, y approaches infinity

[quote]As x approaches 0 in the derivative, y approaches infinity

The derivative is the slope of the tangent line, and so the slope of the tangent line at x=0 is infinity, or the limit as x approaches 0 of 1/x^2 is positive infinity,

0 = 0.... where a line crosses the x or y axis @ 0 is irrelevant.

plus, as graham said 0 = the absence of value...0 is just how we represent that concept

No, the slope of the tangent line would be undefined, not infinity.

= infinity

I don't think you've addressed my point. You are assigning 1/0 a value of infinity when it is infact undefined. You cannot assume a value for y at x=0 because dividing by zero is not a legitimate operation. By dividing by zero you can 'rove' that 1=2 and the like.

Even if an aymptote leans towards a value and suggests a solution to dividing by zero, it has no solution. You cannot tell what the value at x=0 actually is.

What I am trying to point out in the asymptote of the original graph y=-1/x is that when dividing by zero, you can get not only infinity but negative infinity as well just by looking at the graph. Thus -1/0=infinity and -infinity
Even if you say that the derivative is 1/x^2 and not -1/x, then you are saying that 1/0=infinity but not negative infinity? Why not? For if -1/x=infinity and -infinity, then it follows that 1/x=-infinity and infinity.

For you to assume that the value only keeps increasing, then are you not in turn saying that infinity is equal to negative infinity? As I see it, at x=0, the value of y decreases from infinity to negative infinity. But since both of these values lie on x=0, it follows that the value of y also increases from negative infinity to infinity.

plus, as graham said 0 = the absence of value...0 is just how we represent that concept

Lim (1/x^2)
x --> 0

I don't think you've addressed my point. You are assigning 1/0 a value of infinity when it is infact undefined. You cannot assume a value for y at x=0 because dividing by zero is not a legitimate operation. By dividing by zero you can 'rove' that 1=2 and the like.

Even if an aymptote leans towards a value and suggests a solution to dividing by zero, it has no solution. You cannot tell what the value at x=0 actually is.

What I am trying to point out in the asymptote of the original graph y=-1/x is that when dividing by zero, you can get not only infinity but negative infinity as well just by looking at the graph. Thus -1/0=infinity and -infinity

Even if you say that the derivative is 1/x^2 and not -1/x, then you are saying that 1/0=infinity but not negative infinity? Why not? For if -1/x=infinity and -infinity, then it follows that 1/x=-infinity and infinity.

For you to assume that the value only keeps increasing, then are you not in turn saying that infinity is equal to negative infinity? As I see it, at x=0, the value of y decreases from infinity to negative infinity. But since both of these values lie on x=0, it follows that the value of y also increases from negative infinity to infinity.

You do realise that this shows that the limit to the right is infinity but the limit to the left is negative infinity right? Hence it is undefined. Heres quick link; [url=http://en.wikipedia.org/wiki/Division_by_zero]