Why 0.999… is NOT equal to 1 and RECURRENCE is NOT valid in the decimal notation system
Georg Cantor showed that a Countable Set X must have
Injective (one to one) function F:X to N
where N is the set of Natural numbers = {0,1,2,3,…}
One way function f maps every member of X to a single member of N
There can NOT be “more than one way” to map the members of X to the same member in N
Therefor 0.999... = 1 makes the number set uncountable.
Recurrence
Decimal positional number system
Each digit’s position has meaning
Finite number of digits
Rightmost digit implies precision and therefore UNIT INTERVAL
Discrete mathematics does not represent every real number
Recurrence implies infinite number of digits, infinite precision, unit interval of ZERO
Therefore every number is ZERO
NOT a countable set
NOT even Discrete math
