>> http://www.cq.cx/pics/int-led-vi.png
>
> Where do you *find* this stuff??

I did a google image search for "LED VI graph" IIRC.  Easier than trying to 
explain it.

>> Note that for a fixed value resistor this would be a straight line 
>> starting at the origin.
>
> OK, now I'm confused. A graph of current against voltage? But current is 
> completely *determined by* voltage! o_O

Of course it is determined, but it's only a linear relationship (V=IR) for 
resistors.  LEDs are diodes and are certainly not linear, so you need a 
graph.  You could draw a graph for a resistor if you wanted like I said, but 
it would be a bit pointless because we know V=IR for a resistor.

> OK... so... why not an open circuit then? That would have infinite 
> resistence?

Then the input would be equally connected to 0V and V+ with near infinite 
resistances, that's called a "floating" input, because it can be persuaded 
very easily to either go to 0V or V+, depending on the exact details inside 
the IC (and maybe some state of the other inputs, who knows?!).  Best to 
ensure you have at most around 100K of resistance to one of the rails to fix 
the input reliably.

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