## Munkres’ Proof of Well Ordering Property

In Munkres’ Topology the proof for the Well-Ordering Property is stated as follows: I’m having confusion with the first and second underlined part: “Let A be the set of all positive integers n for …

## Using Zorn’s lemma to show a function maps part of a set one to one onto another set

Let \$A\$ and \$B\$ be any two sets. Let \$X\$ be the collection of functions that map a subset of \$A\$ one to one onto a subset of \$B\$. Define a partial order on \$X\$ and use Zorn’s lemma to show that there …

## Show that \$[2,infty)\$ is also uncountable

Question: Assume \$A\$ is the only uncountable set that we currently know of, where \$A= { xin (0,1): x text{ is a decimal fraction consisting only of combinations of 0 and 1} }\$ From …

## Proof that a sequence of set has a set dense somewhere in \$[a,b]\$

Is the following proof correct? Proposition: if we have a sequence of set \$U_i\$ such as \$bigcup_{iin mathbb{N}} U_i=[a,b]\$ then there exist a \$i\$ such as \$U_i\$ is dense somewhere in \$[a,b]\$ …