Are there variations in infinity where some are larger than others, or infinity is the unsurpassable absolute?

Question

Example, for natural numbers, 1,2,3,4,5...............infinity. and for real numbers .

Answer 1

This is the math definition of infinity.

Mathematics The limit that a function is said to approach at x = a when (x) is larger than any preassigned number for all x sufficiently near a. [See source.]

And this definition itself shows just how completely messed up mathematicians are when it comes to infinity. Do you see it? Infinity is a "...limit that a function is said to approach..."

How can infinity be a "limit" when infinity is boundless? Argh.

It is simply wordsmiting to say the function is approaching that limit and it is not ever going to reach that limit. Merely implying there is a limit to approach and that the limit is infinity is pure make believe.

The truth is...math fails to adequately capture what infinity is. Think about it. Any value you give me, I can always give you one bigger. There is no limit (which means an end) called infinity. I mean, now, what's infinity + 1?

Because we have no adequate math to use infinity is one reason string theory became so popular. String theory avoids the infinity that comes from the so-called singularity of treating subatomic particles as dimensionless points. String theory invented something called a Planck length and that's the smallest a particle (the string) can be...no zero's, so no singularity like 1/0 = infinity.

PS: I am familiar with the so-called proofs that one set of infinity is larger than another (e.g., real versus whole numbers). But they really prove nothing except that mathematics cannot properly handle infinity. Boundless is boundless and to say one set of numbers is more or less boundless than the other is simply illogical.

Answer 2

Yes there are 'more' real numbers than natural numbers, even though they are both infinite. Putting aside the philosophy of whether infinity is an object, concept, or what, we say two sets are equal in size if we can pair off the members. For example the natural numbers and the even numbers are the same 'size' since we can pair 0 with 0, 1 with 2, 2 with 4 etc.

However we can never pair the real numbers with the natural numbers, and for a neat (and very easy) proof of this type Cantor's Diagonal into Wikipedia or similar. Therefore, since the naturals are contained in the reals, the set of reals is larger than the set of natural numbers. There are other larger infinities too, and I think the natural numbers represents 'the smallest' of infinities.

Answer 3

Infinity is infinity, it is a arbitrary number that has no value and knows no bound.

However, once calculus is applied and where functions are compared to another in which both functions approach infinity (where the equation grows without bound) there are variations where one function is greater than another. There will be occasions where one function simply approaches infinity faster than the other.

Until you reach that point in calculus, it is safe to just leave inifnity as is where it is simply a "number" which is so large it has no limit.

Answer 4

I dont think so. I mean its just going on forever. Infinite has a start but no end. Although this may not be a "scientific" or "bookexplanation" quality I do make a good point right? Infinite is supposedly a large number that never stops. But yes it can be infinity nothing in a sense but it has to have a starting point. You cant go on forever if you have no point to being the journey. (: I hope this helps

Answer 5

Infinity is not a recognized number. It is a concept. That is the reason for writing R = ( - ∞, ∞ ) and not [ - ∞, ∞ ]
R as an open interval does not include infinity, whereas closed interval includes it which is incorrect because infinity is not a number, but just a concept.

Answer 6

The only two kinds of infinity are positive and negative.

Answer 7

There is no such thing as NOTHING!!!