<?xml version="1.0" encoding="utf-8" standalone="yes"?><rss version="2.0" xmlns:atom="http://www.w3.org/2005/Atom"><channel><title>Open Propositions · Maximum Mathematics</title><link>https://maximummathematics.com/books/foundational-mathematics/logic/open-propositions/index.html</link><description>All of the propositions we’ve dealt with so far have had definite truth values. For example,
$$\text{Thomas Jefferson was the second president of the United States.}$$is a proposition that is known to be false. A statement such as
$$\text{2 + 2 = 4, or 2 + 2 = 5.}$$is a compound proposition that is true.
However, a statement such as
$$\text{$n$ is 1 more than a multiple of 3.}$$is not a proposition, because we don’t know whether it’s true or false. We would need to know the value of $n$ in order to reach such a conclusion. For example, the statement is false when $n = 5$, but true when $n = 16$. Here, we’ll deal with sentences involving variables like this one.</description><generator>Hugo</generator><language>en-US</language><atom:link href="https://maximummathematics.com/books/foundational-mathematics/logic/open-propositions/index.xml" rel="self" type="application/rss+xml"/></channel></rss>