1. ## A quick question about planes

Is a plane parallel with itself?

2. ## Re: A quick question about planes

depends on the definition you're using ...

"Two planes that do not intersect are said to be parallel." ... this definition would say (to me, anyway) a plane is not parallel to itself.

Parallel Planes -- from Wolfram MathWorld

... there is probably another definition somewhere which could be interpreted to say it is parallel to itself.

3. ## Re: A quick question about planes

Originally Posted by Breh
Is a plane parallel with itself?
The answer depends on the definition of parallel one uses. Here are two.
1. If $\Pi_1~\&~\Pi_2$ are two planes the statement $\Pi_1\|\Pi_2$ parallel means they do not intersect.
2. If each $\Pi_1~\&~\Pi_2$ is a plane the statement $\Pi_1\|\Pi_2$ parallel means both are perpendicular to the same line.

#1 is the one Skeeter has given you. And that means that a plane is not parallel to itself.

#2 is used in vector space(analytic geometry). The wording is key. Under #1 we must have two planes.
But in #2 it is possible that $\Pi_1~=~\Pi_2$ so a plane is parallel to itself. Having taught mostly set theory&logic or vectors & geometry when I first read your question I thought. 'well of course a plane is parallel to itself. I am use to using set-theory textbooks that use parallelism as an example of an equivalence relation. Therefore a plane is related to itself(reflective). Moreover, we do want an element to belong to the equivalence class it determines.