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The Archimedean property: any point x before the finish line lies between two of the points P n (inclusive).. It is possible to prove the equation 0.999... = 1 using just the mathematical tools of comparison and addition of (finite) decimal numbers, without any reference to more advanced topics such as series and limits.
Bertrand's postulate and a proof; Estimation of covariance matrices; Fermat's little theorem and some proofs; Gödel's completeness theorem and its original proof; Mathematical induction and a proof; Proof that 0.999... equals 1; Proof that 22/7 exceeds π; Proof that e is irrational; Proof that π is irrational
The Wiki page introduces the proof thus: "There is an elementary proof of the equation 0.999... = 1, which uses just the mathematical tools of comparison and addition of (finite) decimal numbers, without any reference to more advanced topics such as series, limits, formal construction of real numbers, etc. ".
A: 1 can be written many ways: 1/1, 2/2, cos 0, ln e, i 4, 2 - 1, 1e0, 1 2, and so forth. Another way of writing it is 0.999...; contrary to the intuition of many people, decimal notation is not a bijection from decimal representations to real numbers.
OK... I learned about 0.(9) being the same as 1 in high school too... But now I have this question. 1 = 0.99999... right? 2 = 1.99999... every ok so far. does this ...
If (0.999...) is a real number, then it MUST be equal to 1, since there is no such thing as "the number prior to 1" by definition of the reals. Then, let's all agree ...
It is perfectly true that 0.999...999 with any natural number of nines denotes a real number that is less than 1. But "0.999..." is shorthand for saying that there are an infinite number of nines.
1 is a rational number, .999...... is not a rational number. By definition an irrational number is a number which cannot be expressed as a fraction m/n, where m and n ...
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