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0.9999 ... = 1

soroban

Well-known member
Feb 2, 2012
409

They were discussing [tex]0.9999\cdots \,=\,1[/tex] at another site.

My mind (usually linear) slipped a quarter-inch to the left
. . and I came up with this scenario.


Suppose we ignore the fact that: [tex]10 \div 1 \,=\,10.[/tex]

Instead, we say: 10 divided by 1 equals 9 with remainder 1.

Then we have:
Code:
          0.9 9 9 9 ...
        ---------------
      1 ) 1.0 0 0 0 ...
            9
          ---
            1 0
              9
            ---
              1 0
                9
              ---
                1 0
                  9
                ---
                  1
Is that interesting? . . . or just weird?