2007-11-14 04:56:07 · 12 answers · asked by Laurie C 1 in Science & Mathematics ➔ Astronomy & Space
The number of fractions (that is, ratios of integers) between 0 and 1 is countably infinite. However, the number of real numbers between 0 and 1 is uncountably infinite.
2007-11-14 05:45:15 · answer #1 · answered by jgoulden 7 · 0⤊ 0⤋
Let n and n+1 be two consecutive integers > 0 Then 1/n and 1/(n+1) are fractions between 0 and 1 Now there are no integers between n and n+1, but there are an infinite number of fractions between 1/n and 1/(n+1). One such fraction is the average of 1/n and 1/(n+1) = [1/n + 1/(n+1)] / 2 Therefore there are more fraction between 0 and 1, than there are integers between 0 and infinity. Note that integers are countably infinite, while fractions are not
2016-04-04 00:51:59 · answer #2 · answered by Anonymous · 0⤊ 0⤋
A fraction in it self is undefined. A piece of the whole. Like a circle has infinite points. So yes, fractions between any number are infinite!
2007-11-14 05:03:23 · answer #3 · answered by Anonymous · 0⤊ 2⤋
there are n-1 fractions where n=the largest number. Since the number of numbers is infinite, I believe infinite minus one is still infinite, but I could be wrong. It happened once before, back in 1968 when I admitted I was wrong about something, but it turned out later I had been correct all along. ;)
2007-11-14 05:00:04 · answer #4 · answered by John M 7 · 1⤊ 1⤋
Yes, absolutely. You can keep making smaller and smaller fractions forever. Just when you think you have run out, add another digit to the denominator and continue on, forever.
2007-11-14 04:58:37 · answer #5 · answered by LonHolder 3 · 2⤊ 0⤋
Absolutely! Numbers slightly greater than 0 such as .00000000000000000000000000.....1 to number slightly less than 1 such as .999999999999999999999999.....
2007-11-14 04:59:38 · answer #6 · answered by sw_engineer60 4 · 0⤊ 1⤋
Infinitely. How many times can you divide something...
2007-11-14 04:59:07 · answer #7 · answered by Anonymous · 2⤊ 1⤋
Yes, you can always increase the value of the denominator
2007-11-14 04:59:31 · answer #8 · answered by Brian K² 6 · 1⤊ 0⤋
On paper yes, but not in physical practice.
2007-11-14 05:37:27 · answer #9 · answered by xooxcable 5 · 0⤊ 0⤋
yes
2007-11-14 05:05:27 · answer #10 · answered by ? 3 · 0⤊ 0⤋