suppose x=0.9999999.....(k) i.e. constant
so 10x=9.9999999999.......
10x-x= 9 which means 9x=9 and x=1!!!
how comes? i gave statement that
x=0.9999999.... pls explain me!
2007-02-03 23:25:35 · 3 answers · asked by Neo 2 in Science & Mathematics ➔ Mathematics
i thought the same as you but then I saw this site and it was quite amusing. Check it out and it will give you a clearer understanding of the result.
2007-02-03 23:41:31 · answer #1 · answered by LEEANE G 3 · 1⤊ 0⤋
LEEANE G, that is a great site, thanks for the posting.
The mistake all those crackpots writing to the site make is they seem to think math exists in some mystical reality, and it is the job of mathematicians to map out the existing math. People actually seem offended that anyone could believe .9999... = 1.
Math is a set of consistent rules. Period. It can be used to look for real world results, in which case it is applied math, or it can be used just to find consequences of the starting conditions. The fact is that using simple consistent rules, .9999... = 1 both follows logically and is very useful. Is it possible to define an algorithmic system where .9999... != 1? Yes it is. But that is not the one we all learn in school, which is the one we use in physics, banking, and other real-life applications.
Some people find this very nonintuitive. There are some things in science (speed of light, warping of space and time...) which our intuitions are wrong on.
2007-02-04 10:13:28 · answer #2 · answered by sofarsogood 5 · 0⤊ 0⤋
0.9999999999..... without end is the sum of a serie
first term 9/10 and ratio 1/10 S = 9/10+9/100+9/1000+..... =
=9/10( 1+9/10+9/100+....
This sum = 1/(1-10) = 10/9 SO MULTIPLIED BY 9/10 = 1
So 0.99999999....without end =1
2007-02-04 09:28:18 · answer #3 · answered by santmann2002 7 · 0⤊ 0⤋