
Continuous use of Contiguous

Kevin and Rubi have been happily married and in love for over fifteen years and have three great kids. He's a Public Safety Communications Supervisor and a "fantastic fiction" geek. She's a wonderful wife and a great mom, and writes about computer games for a living at Massively.com. Kev and Rubi enjoy spending as much time together as they can given their busy lives.
Posted By kevbayer at 8/22/2006 07:03:00 PM
Continuous use of Contiguous
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3 comments:
Found this post on Google and you rock. My thoughts exactly!
From 'Physics' by Aristotle:
"A thing that is in succession and touches is 'contiguous'. The 'continuous' is a subdivision of the contiguous: things are called continuous when the touching limits of each become one and the same and are, as the word implies, contained in each other: continuity is impossible if these extremities are two. This definition makes it plain that continuity belongs to things that naturally in virtue of their mutual contact form a unity. And in whatever way that which holds them together is one, so too will the whole be one, e.g. by a rivet or glue or contact or organic union."
The following is what I recall from a maths lecture several years ago, so I could be wrong...
(Sorry the graphs don't show up as I need them tho. I don't know how to specify a fixed width font in the comments - hopefully you can figure out how the graphs should look.)
Let's say you monitor the voltage on a wire at times T1, T2 and T3 and your results are (T1:10v, T2:5v, T3:15v).
You graph your results with time on the X-axis and Voltage on the Y-axis.
15v: ___
10v: ___
5v: ___
0v:
T1,T2,T3
It is true to say that Y is continuous for values of X between T1 and T3.
It is NOT true to say that Y is contiguous for values of X between T1 and T3 because the values of Y do not join up with each other.
If the results had yielded the following graph.
15v:
10v: ________
5v:
0v:
T1,T2,T3
or any sort of unbroken curve (a straight line being a specific type of curve) it would be true to say that Y is both continuous and contiguous for X between T1 and T3. Here the use of "continuous" is redundant as it is implicit from the use of "contiguous".
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