What is infinity

[xtraze]

I know that it has no definite value and the highest value if we take in mathematics. But are you having any more Ideas regarding infinity ?

let them out here.

[AfTriX]

If infinity is the highest value, what do we call for infinity + 1?

I mean
infinity + 1 = ????

[TcM]

Infinity is a term with very distinct, separate meanings which arise in theology, philosophy, mathematics and everyday life. Popular or colloquial usage of the term often does not accord with its more technical meanings. The word infinity comes from Latin : "In-finite", is not ended.

This might help.

[John]

If infinity is the highest value, what do we call for infinity + 1?

I mean
infinity + 1 = ????

In programing call that a "type mismatch" error. Infinity is an idea, not a value.

[AfTriX]

Wiki says the following:

The word infinity comes from the Latin infinitas
or "unboundedness." It refers to several distinct
concepts (usually linked to the idea of "without
end" or "bigger than the biggest thing you can
think of") which arise in philosophy, mathematics,
theology and everyday life.

[xtraze]

Then can we say that Gmail is providing infinite Space as its unboundedness and bigger than the biggest thing you can think of as the space changes every second.

So, technically Gmail is providing infinite space for users.

[techni68]

Infinity means without limits

[AfTriX]

infinity + r = r + infinity = infinity
  (-infinity) + r = r + (-infinity) = -infinity
                infinity + infinity = infinity
          (-infinity) + (-infinity) = -infinity
                       infinity - r = infinity
                    (-infinity) - r = -infinity
                       r - infinity = -infinity
                    r - (-infinity) = infinity
             infinity - (-infinity) = infinity
             (-infinity) - infinity = -infinity
        infinity * r = r * infinity = infinity  for r > 0
  (-infinity) * r = r * (-infinity) = -infinity  for r > 0
        infinity * r = r * infinity = -infinity  for r < 0
  (-infinity) * r = r * (-infinity) = infinity  for r < 0
 infinity * infinity = (-infinity) * (-infinity) = infinity
 infinity * (-infinity) = (-infinity) * infinity = -infinity
                       infinity / r = infinity  for r > 0
                    (-infinity) / r = -infinity  for r > 0
                       infinity / r = -infinity  for r < 0
                    (-infinity) / r = infinity  for r < 0
                       r / infinity = 0
                    r / (-infinity) = 0

Where we get into trouble is with defining the following:

        infinity + (-infinity)
     (-infinity) + infinity
        infinity - infinity
     (-infinity) - (-infinity)
               0 * infinity
        infinity * 0
               0 * (-infinity)
     (-infinity) * 0
        infinity / infinity
        infinity / (-infinity)
     (-infinity) / infinity
     (-infinity) / (-infinity)
        infinity / 0 = infinity
    (-infinity) / 0 = -infinity

I found on a site.

[John]

That is interesting but it has no meaning. Infinity is a concept, not a number therefore "r / infinity = 0" has no meaning. Its like saying "r / sidewinder = 0" it just doesn't make sense. I believe the definition of infinity so-to-speak is limitlessness. So

1 / infinity = infinitesimally small number but not zero. Therefore

r / infinity = limit as r approaches 0 of f(r) which does not equal 0.

It is kind of interesting how the single question alone, "what is infinity," is the basis of all calculus!

====

And while we are on the subject of infinity. I would just like to crush another concept. Many people think the universe is continuously subdividable which it isn't! The idea stems from the idea that you can keep halving "things" - something like "If you have an eight ounce cup of water and take half away you are left with 4 ounces, another half 2 ounces, another half 1oz, another half .5oz another half .25oz, and so on..."

The reason this cant be done is because eventually you will only be left with one water molecule. One single molecule of H2O. If you divide that any further you no longer have any water, but it could be broken down into individual atoms and then individual protons, electrons, and neutrons, but at that point you can no longer divide your water in half. (which is one of the ideas behind particle physics)

[WingedPanther]

Infinite can be defined fairly precisely, but is not always a single "value". For example, there are infinitely many integers, and infinitely many real numbers, but using mappings between them, it can also be shown that there are more real numbers than integers. This leads to the concept of "levels of infinity". Depending on the axioms chosen for the set theory under use, these levels of infinity can either represent discrete jumps or a continuum. For a model with discrete jumps, they are generally represented as aleph-nought, aleph-1, aleph-2, etc. This is all based on the concept of cardinality, or measuring the size of a set.

For a different perspective, if you have the set of all subsets of the non-negative integers where each subset contains 0-n, for some integer n, then that set can be considered "infinity". If you union that set with the number 1 (not {1}), then the new set can be viewed as infinity+1.

Doing some searches on "set theory" and "Cantor" can give you more information.