dear RIA: i bring you...a paradox!

[Delta1212]

Here's an infinity paradox.

If you have an infinitely long line, any point you choose will be the midpoint, as the length of the line to either side will exactly equal the length of the other side. Of couse, if you were to cut, say, three feet off of one of the halves, it would still make up exactly half of the line as it would still equal the legth of the other side. But now the two ends no longer reach each other.

In other words, take an infinite line, and cut it in half. Remove a a section from one of the halves so they no longer reach. Each one is still exactly the same length (infinity). This means you still have the same total length, but the two sides no longer reach each other.

[Grand Poobah Marx]

Noice!

[Lamentations]

Each one is still exactly the same length (infinity).

But isn't saying this fallacious anyway, seeing as infinity is not an exact thing :/ It is more arbitrary, like you can't divide infinity by something.