0
votes
1answer
103 views

Are all uncountable infinities greater than all countable infinities? Are some uncountable infinities greater than other uncountable infinities? [duplicate]

I recently finished a discrete mathematics class, and near the end of the semester, the prof (very superficially) touched on countable and uncountable infinities. His explanation of countable ...
0
votes
1answer
36 views

Number of k-permutations that have odd number of an element

I want to find a recurrence relation $h_k$ for the number of k-permutations of $\{\infty a,\infty b, \infty c, \infty d \}$ that have an odd number of a's. I let $h_0=0$ because there is no odd ...
11
votes
4answers
445 views

Partitioning the naturals into an infinite number of large sets

Is it possible to partition the positive integers into an infinite number of disjoint large sets ?
1
vote
1answer
95 views

Finding an element of the intersection of an infinite sequence of “compatible” sets of infinite sequences

Let $A$ be a set. Let $A^\omega$ denote the set of infinite sequences of members of $A$ (i.e., functions from $\omega$ to $A$). Define $\omega_n = \omega \setminus \{n\}$. Let $A^\omega_n$ denote the ...
0
votes
0answers
100 views

How to observe infinity?

In my calculus course, there's example stated on the book: Given that $M$ is an ordered set and the sequence $\{a_n\}\subset M$, prove that there's a (weakly) monotonic subsequence of $\{a_n\}$. ...
2
votes
4answers
265 views

An infinite set having “one more element” than another infinite set

A classic example of homeomorphism is between a sphere missing one point and a plane To see this, place a sphere on the plane so that the sphere is tangent to the plane. Given any point in the plane, ...
3
votes
3answers
4k views

Isn't there a bijection between real numbers and natural numbers?

I'm not a math guy and probably this is a stupid question. However, I was browsing Wikipedia out of curiosity and I could not understand this one statement: [...] not all infinite sets have the ...