What's bigger, an infinity, an infinity and one or an infinity of infinity's?

Question

What's bigger, an infinity, an infinity and one or an infinity of infinity's?

Answer 1

The answer is hinted at in Andrew E's first sentence of the second paragraph.

Taking not only any finite number of things from infinity, but also taking an infinity any infinite number of times from it leaves infinity. To illustrate: there is a line with an infinite number of, say, beads strewn all over it. Somebody is allocated ,say,every tenth bead, somebody else every hundreth, still another every thousandth, and so on to infinity. All will have an infinite number of beads, because, in all cases, since the line is infinite, there will be no end to the process of the distribution of the beads, this leaving  the non-allocated beads also infinite.

We can apply mathematical- and philosophical-sounding phrases like: Infinity less Infinity equals Infinity, a fraction of Infinity is equal to Infinity and taking away the Infinite from the Infinite, the remainder is Infinite. l

Answer 2

Infinity is not a number, so you can't add one to it or have an infinity of infinities.  Nor is there any such thing as "an infinity"; that is, it's not a thing.  One could say that infinity is the lack of finiteness, lack of boundaries, though that's not a very good definition either.  It's the emptiness that allows us to perceive something finite.  Finite/infinity go together like solid/space or sound/silence.  We can't imagine or perceive solid without reference to space or space without reference to solid.  Likewise we can't imagine a finite number without reference to infinity.  This is harder to see because it's more abstract, but I think it's true.  And we can only seem to imagine infinity in terms of finite numbers--which leads us to notions such as infinity plus one.  That's really just imagining a very high number and adding one to it.

Answer 3

if you think about the meaning of infinity, infinity and zero are the same

Answer 4

philosophically speaking?

Infinity minus one -

- pure without ego.

Answer 5

technically infinity add one is the same as infinity as infinity goes on and so it willl encompass any additional numbers

Answer 6

One infinity

Theres only uno infinity

I-I-In -fin itee

Theres only uno infinfity -

(football chant?)

There might be a squillion infinities for all those parallel universes?

Answer 7

This question was answered in 1886 by Georg Cantor, who in the process of laying the foundations of Set Theory, also answered many questions about infinity.

Infinity is when there is so many of something that taking any finite number of things away from it (or adding any finite number of things to it) will not change its size.  So infinity is the exact same size as infinity plus one.  Furthermore, infinity multiplied by infinity is also the same size as infinity, so the answer to your question is that all the options you listed are the exact same size.

However, there is more than one size infinity.  In fact, there are an infinite number of infinities.  The smallest infinity is called the "countably infinite", such as the number of integers.  We don't know what the next one is, but it is uncountable.  Cantor hypothesized that the next size was 2 to the power of infinity, but we have since learned that whatever the order of infinities is, we can never know it.  Cantor's Hypothesis was proved to be unprovable by Godel and Cohen in the early 20th century.

Answer 8

Believe it or not, work has been done in this area.

There are different values of infinity.

Wiki 'Aleph Null' Cantor

Answer 9

Forget about the work of Cantor. He progressed mathematics not philosophy.

As the post above states: infinity is nothing.

Nothing is infinity. Nothing is everything. And nothing.

Infinity has no shape, size or form. No size=no bigger.

Answer 10

Infinity in "ordinary" usage is generally considered to be an extension of the sequence of "ordinary numbers". Infinity is not a number itself, and can't really be treated as one. So you can't define Inf.+1 or 2 x Inf., meaning that you can't sensibly talk about Infinity+1 being greater than Infinity.

However, as Andrew E remarks, the mathematician Cantor found some remarkable properties about the different possible kinds of Infinity, which can in some sense be compared for "size".

The first kind of infinity is the "countably infinite" kind. This is fairly easy to recognise. For example, the natural numbers 1, 2, 3, 4, etc are countably infinite. So, too, are the even numbers 2, 4, 6, 8, and so  on.  By "countably infinite" is meant that you can label each one in turn by a number, without missing any out or running out of label numbers.  Hence

Even numbers: 2, 4, 6, 8, 10,

Counted as.....: 1, 2, 3, 4, 5, ...

In this way, you can label each even number with a "natural" number, and however far you go, you can always do this. There's never an even number you find between two adjacent numbers that you can't label, or count, in this way.

There are infinitely many even numbers, but infinitely many natural numbers, and though intuitively you might think there are more natural numbers than even numbers, the "size" is the same - infinite.

You can also do this "counting" with fractions, of the form a/b, for example, 1/2, 2/3, 2/4. 3/4, and so on. It is possible to construct a scheme for labelling every fractional number with a natural number, without missing any out. I won't do it here, but it's easy enough to find this on the web.

However, you can't do with with the set of all decimal numbers, that is, numbers of the form 3.14159265... or 1.33333 and so on. It can be shown that if you try to create a labelling scheme to account for all decimal numbers, it's possible to construct a new decimal number between any two others that cannot be labelled by a natural number. It sounds complicated, and in truth it requires a bit of familiarity with number theory to grasp it, but it shows that there is a new kind of infinity, called (naturally enough) "uncountably infinite", which is larger than the "countably infinite" kind.

This is the sort of stuff that Cantor worked on.

Answer 11

I wonder, is infinity endless space & time, or no space & time? Personally, I think it to be the later, a concept we really can not conceive well since we apparently perceive space & time right now.

Blessings!

Answer 12

Infinity, always 1 in front of you, no returns!!!

Answer 13

yeah what Andrew E said...

Answer 14

Infinity's just infinity. It means it goes on and on. You can't add one etc

Answer 15

God's bigger than all of them =]

Answer 16

Infinity raised to the power of infnity squared is infinitely bigger.

Answer 17

What's bigger?

Let's do the math!

1=1

1+1=1

1+1+1=1

Are we confused yet?

Infinity encompasses everything!

Infinity + Infinity = Infinity

Don't you just love synchronicity?

Time and space can indeed be confusing, is it not so?

Clarity and Wisdom, define Infinity!

Answer 18

Technically, if you view an infinity as an increasing number without end or an unattainable quantity, this question becomes a mere illusion.  All three would be the same size.

Answer 19

infinity. there is no such thing as infinity plus one. infinity is forever and has no end. this is a hard concept for some people because they cannot imagine such a thing. it is almost unimaginable.