I have great difficulty fathoming a difference between the infinite of 'infinitely large' and the infinite of 'infinitely long', or the infinite of 'infinitely stupid', or even the infinite of 'infinitely happy'.
I honestly don't see the difference in the infinite concept... all the more so as something infinitely long would also be infinitely large, and something infinitely large would also be infinitely long.
Anyway, it is because of our numbering system (base ten) that we cannot perfectly represent 1/3, 1/7, etc. I made that point in a post somewhere on page #12 I'd guess. The fractions are very simple, quite perfect to be honest. If I have a pie, and I cut it into 3 equal pieces: 1/3 x 3/1, 100% of the pie. I cannot represent this number as perfectly with a base ten system however, and the closest accuracy I will be able to attain is .3^ x 3, 99.9^% of the pie.
This isn't a problem with the faction, and we know intuitively that 100% of the pie was really eaten... but we need to recognize that there is an infinitesimally small gap before we attain 100%. This is not because you can't divide one thing into 3 pieces (you usually can)... it is because the base 10 system (while simple) has limitations. I find that our knowledge more often advances from questioning answers, then from answering questions. That we have established our numbering system neither makes it perfect nor makes oversights go away.
I honestly don't see the difference in the infinite concept... all the more so as something infinitely long would also be infinitely large, and something infinitely large would also be infinitely long.
Anyway, it is because of our numbering system (base ten) that we cannot perfectly represent 1/3, 1/7, etc. I made that point in a post somewhere on page #12 I'd guess. The fractions are very simple, quite perfect to be honest. If I have a pie, and I cut it into 3 equal pieces: 1/3 x 3/1, 100% of the pie. I cannot represent this number as perfectly with a base ten system however, and the closest accuracy I will be able to attain is .3^ x 3, 99.9^% of the pie.
This isn't a problem with the faction, and we know intuitively that 100% of the pie was really eaten... but we need to recognize that there is an infinitesimally small gap before we attain 100%. This is not because you can't divide one thing into 3 pieces (you usually can)... it is because the base 10 system (while simple) has limitations. I find that our knowledge more often advances from questioning answers, then from answering questions. That we have established our numbering system neither makes it perfect nor makes oversights go away.
Please give me a home where cloud buffalo roam
Where the dear and the strangers can play
Where sometimes is heard a discouraging word
But the skies are not stormy all day