where the no 1 is comming from ?

Question

OK we all know that if we add something with no "0" someday it will reach to no "1",
then what u will say about this???
0.0
+0.9
-------
0.9
+0.09
---------
0.99
+0.009
-------------
0.999
+0.0009
-------------
0.9999
if we add in this way when the no "1" will come???
and same

1.0
-0.9
------
0.1
-0.09
---------
0.01
-0.009
----------
0.001
-0.0009
-------------
0.0001
when the no "0" will come????

Pls sumit you thaughts.

Answer 1

Given,

S = {0 + 0.9 + 0.09 + 0.009 + ... }

Consider,

10S = 10 {0 + 0.9 + 0.09 + 0.009 + ... }


10S = 0 + 9 + 0.9 + 0.09 + 0.009 + ...

10S = 9 + {0 + 0.9 + 0.09 + 0.009 + ... }

10S = 9 + S

9S = 9

S = 1

If the sequence continues to infinity, S will be equal to 1 by the process of limits.

Answer 2

METHOD 1

If you know how to sum a geometric series you can confirm that 0.99999999....
= 9/10 + 9/100 + 9/1000 + .....
= 1

METHOD 2

If not, think of it this way
0.9 is less than 1
Can you find a number that is greater than 0.9 and less than 1 ----- Yes - 0.95

0.99 is less than 1
Can you find a number that is greater than 0.9 and less than 1 ----- Yes - 0.995

0.999 is less than 1
Can you find a number that is greater than 0.9 and less than 1 ----- Yes - 0.995

If 0.99999.... is less than 1, there must be a number that exists between these two values. If you cannot find one, it must mean that these numbers are equal.


METHOD 3

1/3 = 0.3333333333333......
2/3 = 2 * 1/3 = 0.6666666666666666.........
3/3 = 3 * 1/3 = 0.9999999999999999.........
But 3/3 is 1
Therefore 0.999999999...... = 1

By the same arguments, you can prove that the limit as x approaches infinity of 1/(10^x) is 0.

Answer 3

This is the same as saying if you bite half of your sandwich, then half of the remaining part, and keep biting half of what you have will you ever finish?

Theoretically, no, and the same for your paradox, you will never reach 1, but we know that you will eat the last piece of your sandwich whole, and on the nines you will stop at the 50th one and say, ok this is close enough to 1, and a decimal and 50 zeros then a one, is essentially 0 in real life.
Greek philosophers were aware of similar paradoxes and there have been solutions proposed to the questions they posed similar to yours. Read more at this website for other interesting questions and answers.

Answer 4

Jews do no longer believe that Jesus is the messiah. we are waiting for the messiah to get right here. Christians are waiting for the 2d coming using fact they are waiting for the return of the messiah. in accordance to Judaism, the messiah could do here staple products: a million) deliver at the same time all of the Jews to Israel. 2) He could rebuild the temple in Jerusalem. 3) There could be international peace. Jesus did no longer fulfill ANY of those. There are extremely some different issues the messiah could be or fulfill, yet those are some absolute fundamentals. it is likewise very sparkling to make certain that Jesus did no longer do any of those issues.

Answer 5

subsequent addition of decimal 9 will never give 1 , it will only give a number which approximates to 1,
similarly subsequent subtraction of decimal 1 will never give 0 but a number which approximates to 0

Answer 6

0.9 repeating equals 1. I'll bet a dollar on it.

http://polymathematics.typepad.com/polymath/2006/06/no_im_sorry_it_.html

Answer 7

0?