TiredJim

I'm not sure if this has been brought up, but infinity is a mathematical idea. It's not a number or a position.

Saying something is "infinitely close to zero" is used in equations like f(x) = 1/x, because this function doesn't exist at zero (can't divide a number by zero), but any x to the left or right of zero works. So, you say the limits from the left and right are zero, and so x's for both sides become infinitely close to zero.

However no real number is infinitely close to zero, because if you pick two real numbers, then their distance is measurable.

In other words, you are correct, no two actual numbers are infinitely close to each other.

This is from a mathematical perspective, which isn't quite the same as a physics perspective, which I don't really know.

It's possible because .999 (to infinity) converges to 1 just as .333 (to infinity) converges to 1/3. You can't use one infinite sum to disprove another. That's just playing on people's ignorance when it comes to math.

As to your attempt to tie it into god, well, that's entirely ridiculous and irrelevent.

Demosthenes

"Infinitely close" also occur all the time in plain old fashioned algebra with asymptoes. The reason why we say something is getting infinitely close to something is because we use real numbers in algebra and calculus.

A way you can think about this is to visualize the number line that's a subset of the reals.

Say you start with the points 1 and 2 on the line, what's a number that's between 1 and 2? Say 1/2, it'll satisfy the requirement. Now what's the number between 1 and 1/2? 1/4 will work too. Now how about between 1 and 1/4? 1/16 will work just as well. Now keep on dividing the line. Will you ever come to a end? The answer is no because we're using the real number line. So between any two given real numbers, there are an infinite number of reals. So say in an algebraic or calculus analysis you're observing that a quantity is approaching 1 but it never reaches 1 because the quantity keep hitting a value that's greater than 1 but steadly less than the previous value. We say that the quantity is approaching one infinitely.

You see it often when you're graphing functions such as a hyperbola. The twin curves will approach a value but they don't quite hit that value, instead they approach infinite as they converge on the value.

paul30

In math there are limits. For example, hyperbolas approach their asymptotes. They never actually reach them, but they get closer and closer forever.

You can set the conditions such that a limit is reached, and for certain purposes, the two things join.

But this is math, which has limited application to reality.

I think two objects can get infinitely close only in a singularity, where even the distance between intraatomic particles close, and then the particles themselves crush.

ex-xian

How is what possible? The number 0.999... is equal to 1. If you're familiar with infinite series and summation notation, I can explain to you how. If not, take 1.5 = 3/2 = 1/2 + (1/2 + 1/4 + 1/8+ 1/16 + 1/32 + ... off to infinity) years of calculus. If you're not willing to do that, then just trust me.

Darth Dane

as teh other guy said, it converges onto 1

Yet a child will see (1) as something wholly dofferent than (0.9999)

The symbol is NOT the same ergo different




DD - Love & Laughter

ex-xian

You and a child may see it, but that doesn't make it true. A child sees dragons in the clouds, but that doesn't mean they should wear fire-proof undergarments.

The symbols, 1 and 0.999..., are different, but the concepts that they represent are identical. Just as the symbols 10/2 and 5 are different, but they still represent the same concept.