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I'm asked to show that the real projective line, P1, is orientable. I'm not quite sure how to define orientable to prove this.

Thanks.

Annnnnet
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    Presumably you were given a definition of what being orientable means if you were asked to prove that something is orientable! If not, please do ask the person that asked you to do this for a definition! – Mariano Suárez-Álvarez Mar 02 '15 at 05:39
  • I was not given a definition! :/ I guess the teacher thought it was obvious, right nos I can't ask him what he meant and I'd Like to try and solve the problem with something better that wikipedia... – Annnnnet Mar 02 '15 at 05:54
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    No, it is not obvious. In fact, unless you tell us what the context of the problem is we cannot even know what sort of definition you are expected to use. This is a problem in a course on projective geometry (as you tagged), in algebraic topology, in differential geometry? What you'd do in each of these cases is different... The very beest you can do is wait until you hav him at hand and ask him. That's what he is paid for, in fact! – Mariano Suárez-Álvarez Mar 02 '15 at 05:57
  • It's projective geometry – Annnnnet Mar 02 '15 at 06:04

1 Answers1

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By one point $P$, a projective line is not divided into two segments.
Only two point $P, Q$ divide it into two segments.
A third point $R$ lies in one of these two segments.
This is the concept of orientation or simply direction on the line: there are two possibilities of the order of the points, namely: $PRQP$ or $PQRP$.
Draw the line e.g. as a circle to illustrate this.

Gerard
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