WhiteKnight
Registered Member
And what would the lengths of said sections be?Originally posted by leeaus
Neither section encompasses the length of a dimension. Thus each section is finite.
And what would the lengths of said sections be?Originally posted by leeaus
Neither section encompasses the length of a dimension. Thus each section is finite.
A fine quote, but not a meaningful answer to WhiteKnight's question. If something's finite, it can be counted. Whether or not it 'counts' (ie. matters) doesn't affect the fact that it has a length by way of being finite.Originally posted by ProCop
"Not everything that can be counted counts, and not everything that counts can be counted."
- Albert Einstein (1879-1955)
And what would the lengths of said sections be?
If the length is finite, it has a specific number.Originally posted by ProCop
Well the question cannot be answered by a specific number
Having a length or size does not imply finiteness. 'Infinite' is a valid length.Originally posted by ProCop
The only way I figure is that to be comparable they (both) have to have a size (otherwise they would be uncomparable). It implies finiteness (of unspecified length).
If the length is finite, it has a specific number.
I don't care how you measure it. Whether your equipment gives you 0.1% error or 100% error doesn't change the fact that the thing being measured still has a particular length that's independent of your measurement.Originally posted by ProCop
Not true.
If the length of a line is finite then such length can only be approximated (considering the unpreciseness of any meassuring equipment). What’s more really exact length would need an infinity of digits behind the decimal point (to be “exact”)).
The most far one can get in “meassuring/describing” a line is then an approximation of line's length. Such approximation of the length of a line sayes that eg. line l is longer then 10 cm and smaller then (eg.) 10.00000000001 cm. That’s a fair description of finite length.
Your reasoning fails in assuming that because Ls < Li, Ls is necessarily finite. For example, the cardinality of the set of real numbers is greater than the cardinality of the set of integers, but both cardinalities are infinite.Originally posted by ProCop
Thus what I stated above holds its stand because the section Ls of an infinite line Li can be easily approximated namely
Ls > 1 cm
And
Ls < Li
That makes Ls pretty much described as finite and I do not really see what you are complaining about.
Your reasoning fails in assuming that because Ls < Li, Ls is necessarily finite. For example, the cardinality of the set of real numbers is greater than the cardinality of the set of integers, but both cardinalities are infinite.
It is to the point. The point it illustrates is that just because something is smaller than infinity does not make it finite, as you were claiming.Originally posted by ProCop
It was accepted in this thread to contemplate the (in)finity of lines on the scale of numbers. The set chosen was positive numbers and it is OK to compare sets as an example. But your comparition is not really to the point.
I'm not going to argue about measurements. We've been talking about a conceived, mathematical space, not physical reality.Originally posted by ProCop
Please consider (again)
L line size L > 10 cm and L < 10.00000001 cm. The extact size of L cannot be expressed in numbers becase if we want to know <i>exact</i> size of the line we would need an infinite digit eg. 10.0000000000000055354457955...............infinity. <i>Exact</i> size of L (I egree that L has an exact size as you proposed) is not available in numbers (The extact distance from the first to the last point of L would require counting in infinitesimals (while attempting to get the required number with total precision) . (We can only specify that the line L is longer > 10 cm and L < 10.00000001 cm)
Again, the same as I put forth above. Just because Ls is not as long as the infinite line Li (as you constructed at the beginning of the paragraph, I'm not sure why you made it finite at the end), does not make it finite. That is the reason for the comparison between cardinalities I presented last post - to show that not all infinities are the same size.Originally posted by ProCop
Ditto happens with line Ls which is a section of an infinite line Li.
The <i>exact</i> size of Ls is in macro-terms-uncertainty comparable to the micro-terms-uncertainty about the numerical representation of the size of L (from the previous alinea). Only the uncertainty of L’s size lies in infinitesimals while the uncertainty of Ls lies in the oposite of infinitesimal let's call this oposite "infinitegreatmals" (Very Biggy Big Numbers). But both lines (L and Ls) are finite, because L doestn’t reach 10.00000001 cm and Ls doesnt’ reach the size of Li. (L is not longer than 10.00000001 cm and Ls is not longer than Li – they both have unspecified length but they both are finite)
Would infinitesimal be the word you are looking for.
It refers to numeracy more so than distance.
Time is something that does need units to exist. Its basic unit is an observation of a return to a previous situation.
Distance is not really related to that is it.