Prove the Cordinality of the sets ... are equal?

Question

How can I prove the cordinality of the sets of even, odd, and natural numbers are equal?

Thanks in advance!

Answer 1

Place them into one-to-one correspondance with each other. For instance, you can map the natural numbers onto the evens by the mapping e=2n, or onto the odds with o=2n-1. Verifying that these mappings are one-to-one and onto is left as an exercise for the reader.

Answer 2

Either the four chief points of the compass (north, east, south, west), or the four chief zodiacal constellations which have descended to us from antiquity as Aries, Cancer, Libra, and Capricorn, though due to the precession of equinoxes these constellations shift as the ages pass. These four points are connected with the four arms of the equal-armed cross or with the swastika, as also with the cube -- the four points with zenith and nadir added.



Cosmically the four cardinal points represent a certain stage of manifestation where the three become four, in this case the number of matter. The Zohar says that the three primordial elements and the four cardinal points and all the forces of nature form the Voice of the Will, which is the manifested Logos. The Dodonaean Zeus includes in himself the four elements and the four cardinal points. Brahma is likewise four-faced.



The pyramid is the triangle repeated on the four cardinal points and symbolizes, among other things, the phenomenal merging into the noumenal.



The four cardinal points are presided over, or are manifestations of, four cosmic genii, dragons, maharajas -- in Buddhism the chatur-maharajas (four great kings) -- hidden dragons of wisdom, or celestial nagas. Hinduism has the four, six, or eight lokapalas. In the Egyptian and Jewish temples these points were represented by the four colors of the curtain hung before the Adytum.


See also EAST; NORTH; SOUTH; WEST

Answer 3

all the three are infinite sets, so their cordinality has to be infinity in each case. When u r talking about infinity, comparision is meaningless. for example infinity + 1 is still infinity.

But you CAN say that as the cardinality of all three of thm is infinity, it is equal.