# cardinality

1. ### Cardinality of subsets of naturals

Hi there, here's one question that's bugging me nuts. Cantor defined different kinds of infinity, named aleph_0, aleph_1, ..., each one the size of the powerset of a set of the previous size. The naturals, and therefore all infinite subsets of it, are countably-infinite with cardinality...
2. ### Limits' and reals' cardinality

Does the limit function relate to a maximum cardinality? Does the set of real numbers, as they are an "absolute" continuum? Can one map the set of real numbers onto a finite surface? By bijection?
3. ### Cardinality of union of two sets proof

Hello all I am not able to write a proof of the property n(A \cup B) = n(A) + n(B) - n(A \cap B) . I was just able to draw sets diagram and one or two steps attached. Please help me with the proof.
4. ### Cardinality

How many k satisfy \;2^n -n=k^2 Example , 2^7 -7=11^2 \; n,k \in N
5. ### Sets (cardinality)

What is meant by odd and even cardinality in set theory. What are formulas to use them?
6. ### find cardinality of superset from its subsets with |6|

did I solve this correctly? problem: |{X: XâˆˆP(B), |X| = 6}| = 28, find |B| solution: C(n, 6) = n! / 6!(n - 6)! = 28 C(8, 6) = 28 |B| = 8
7. ### Finding the cardinality of an orbit of an element

Let A=(123â€¦n)A=(123â€¦n) be an element of PnPn. So that the group PnPn acts on itself by means of the action of conjugation, for BâˆˆPnBâˆˆPn, Bâ‹…A=BAB(^âˆ’1). Stabilizer of A is a subgroup; {A^c âˆ£c=0,â€¦,nâˆ’1}. I want to find the cardinality of OrbPn(A). So by applying the...
8. ### Cardinality of all operations on rational numbers

What is the cardinality of all operations of addition, multiplication and exponentiation upon rational numbers?
9. ### Cardinality of the set of decimal numbers

Cardinalities of the set of decimal numbers and â„ are discussed using denominator lines and rational plane. On the rational plane, a vertical line is referred by its abscissa M. Because the points of a vertical line represent the quotients i/M which have the same denominator M, the vertical...
10. ### I don't think "Infinity + 1" is possible in math

Hello good people of the math world! I was recently having an exchange with a mathematician about infinity-related ideas. I don't know math. But it seems to me that the statement "infinity + 1" is not possible in math. Which means that neither is "infinity + 1 = infinity" and many other...
11. ### |A| â‰¥ |B| and |A| â‰¤ |B| implies |A| = |B| for finite sets

(1) |A| â‰¥ |B| and |A| â‰¤ |B| implies |A| = |B| for finite sets A and B |Â·| and card() denote cardinality of whatever is inside. Proof: Because of (1), there exist bijections f and g: f: A -> f(A), f(A) subset B, g: B -> g(B), g(B) subset A. From f(A) subset B, I apply g to...
12. ### |A| â‰¥ |B| and |A| â‰¤ |B| implies |A| = |B| for finite sets

The title says it all, |Â·| denotes cardinality of the set inside. Proof. Near the end I didn't state the obvious, that is: |A|â‰¤|B|â‰¤|A| \implies |A| = |B|. And I apologize for taking a screenshot and not just copying the entire thing and pasting it here in LaTeX. If that's a...
13. ### Hidden assumption of the diagonal argument

This article uncovers a hidden assumption that the diagonal argument needs, then, explains its implications in matter of infinity. The use of the diagonal digits imposes a condition unnoticed until now. If this assumption were found false, the conclusion of the diagonal argument should be...
14. ### Which infinity for irrational numbers?

The value of a decimal number depends on the number of its digits. For irrational numbers that have infinity of digits, their values seem to be definitive. However, the meaning of infinity is ambiguous because there exist several kinds of infinities. If the infinity used to define the number of...
15. ### Continuous set and continuum hypothesis

This article explains why the cardinality of a set must be either Aleph0 or |â„|. 1. Rational numbers are discrete 2. Real numbers are continuous 3. Collectively exhaustive and mutually exclusive events 4. Continuum hypothesis 5. Cardinality of discontinuous subsets of real numbers...
16. ### Cardinality of the set of binary-expressed real numbers

This article gives the cardinal number of the set of all binary numbers by counting its elements, analyses the consequences of the found value and discusses Cantor's diagonal argument, power set and the continuum hypothesis. 1. Counting the fractional binary numbers 2. Fractional binary...
17. ### Cardinality of generated sets

Hi , let $B$ be a Boolean algebra and $X \subseteq B$ a set. Can I proove that the cardinality of $X$ is the same as for the generated Boolean subalgebra by $X$ (that is: \$\langle X \rangle = \{\bigvee_{i=1}^n \bigwedge_{j = 1}^{k_i} x_{j_i}^{\epsilon_{j_i}}: where \: x_{j_i} \in X \: and \...
18. ### Boolean algebra (cardinality)

Hi, I'm reading this article for the moment: Remarks on contact relations on Boolean algebras (PDF Download Available) And I have a few questions concerning lemmas 4.2, 4.3 and 4.4. If you could help me, it would be great. (btw, sorry for my bad english, I do my studies in french... :) )...
19. ### Cardinality of transcendental numbers

I was reading another thread and I came up with a question. I have no idea how to approach this. A transcendental number is defined to be non-algebraic, that is, it cannot be formed as a root of a polynomial with rational coefficients. This covers complex numbers but let's just deal with...
20. ### cardinality of demonstration of a given theorem

Hi all, sorry if my English is bad. I was talking in an Italian forum of math and no one knows whether it's possible to find a solution to this problem, so I came here... I don't know the correct section, so I put it here. If you have some hypothesis and a thesis find if there are: A) infinite...