Can infinity be greater than infinity?

If you have nothing.

And then double what you have.

Does that mean zero can be different amounts?

No, OP

stick with eharmony wrote:

If there are an infinite amount numbers between 0 and 1 then there is twice the infinite amount of numbers between 0 and 2. Doesn't that make all infinite number unequal then?

Yes

Infinity is not a number, therefore your question is meaningless.

Infinity is a mathematical concept and thus the OP's question has relevance. Infinity is defined on the perspective and context of the mathematical question at hand. The constrained set of infinite numbers contained within one set can smaller than the unconstrained set of infinite numbers contained within a more expansive set.

DaveyGuy wrote:

stick with eharmony wrote:

If there are an infinite amount numbers between 0 and 1 then there is twice the infinite amount of numbers between 0 and 2. Doesn't that make all infinite number unequal then?

http://www.ask.com/wiki/Georg_Cantor?o=2850&qsrc=999&ad=doubleDown&an=apn&ap=ask.com

for a different perspective, check out

[my wife and I agree on many things, but she really likes axiomatic set theory whereas I, in my heart of hearts, don't believe in the whole "orders of infinity" thing.]

stick with eharmony wrote:

If there are an infinite amount numbers between 0 and 1 then there is twice the infinite amount of numbers between 0 and 2. Doesn't that make all infinite number unequal then?

No, that doesn't make all infinite numbers unequal.

Let Q be the set of all rational numbers (meaning numbers that can be expressed as a fraction) and let N be the set of all the natural numbers (meaning {1, 2, 3, ...}). Let |S| denote the cardinality (meaning number of elements) of a set. Q and N are different infinite sets, but Q| = |N|.

Why? Because you can set up a 1-to-1 correspondence between elements of the two sets. Here's a graphic that illustrates how you can iterate through all the rational numbers:

. So there's a 1st rational number, a 2nd rational number, a 3rd rational number, etc. That graphic is equivalent to a mapping that goes like

1-->1/1

2-->2/1

3-->1/2

4-->1/3

5-->2/2

6-->3/1

7-->4/1

8-->3/2

[etc.]

A tiny circle and a large circle are both the same infinity.

Yes.

Infinity + Infinity

mellon wrote:

Infinity + Infinity

I'll see your Infinity + Infinity and raise you a power set of Infinity.

African_Penguin wrote:

jamin wrote:

No, that doesn't make all infinite numbers unequal.

Let Q be the set of all rational numbers (meaning numbers that can be expressed as a fraction) and let N be the set of all the natural numbers (meaning {1, 2, 3, ...}). Let |S| denote the cardinality (meaning number of elements) of a set. Q and N are different infinite sets, but Q| = |N|.

Why? Because you can set up a 1-to-1 correspondence between elements of the two sets. Here's a graphic that illustrates how you can iterate through all the rational numbers:

http://personal.maths.surrey.ac.uk/st/H.Bruin/image/rationals-countable.svg

. So there's a 1st rational number, a 2nd rational number, a 3rd rational number, etc. That graphic is equivalent to a mapping that goes like

1-->1/1

2-->2/1

3-->1/2

4-->1/3

5-->2/2

6-->3/1

7-->4/1

8-->3/2

[etc.]

Yes.

This is all true. The infinity of rational numbers is equal to infinity of integer numbers. but the infinity of irrational numbers is greater than that of the integer and rational number infinites, this is due to listable and unlistable infinities. see

for a description that i could not fully explain in this text box.

All infinities are equal. It's just that some are more equal than others.

infinity cannot be grasped, only pondered

See the Wikipedia article on Georg Cantor. In fact the OP is in good company in his confusion and ignorance.

Here's an excerpt:

Cantor established the importance of one-to-one correspondence between the members of two sets, defined infinite and well-ordered sets, and proved that the real numbers are "more numerous" than the natural numbers. In fact, Cantor's method of proof of this theorem implies the existence of an "infinity of infinities". He defined the cardinal and ordinal numbers and their arithmetic. Cantor's work is of great philosophical interest, a fact of which he was well aware.

Cantor's theory of transfinite numbers was originally regarded as so counter-intuitive – even shocking – that it encountered resistance from mathematical contemporaries such as Leopold Kronecker and Henri Poincaré and later from Hermann Weyl and L. E. J. Brouwer, while Ludwig Wittgenstein raised philosophical objections. Some Christian theologians (particularly neo-Scholastics) saw Cantor's work as a challenge to the uniqueness of the absolute infinity in the nature of God – on one occasion equating the theory of transfinite numbers with pantheism – a proposition that Cantor vigorously rejected.

I'm a Kronecker man myself - "Die ganzen Zahlen hat der liebe Gott gemacht, alles andere ist Menschenwerk". You tell 'em, Leopold.

inf + 1 = inf

Infiniti Q70L > Infiniti G