More about .0.999…
Summary
The article “More about .999…” explores the mathematical meaning of the infinite decimal 0.999… and why mathematicians consider it exactly equal to 1. The author explains that the difficulty comes from confusing a number with its written representation (a numeral), and shows different ways to understand infinite decimals, including adding them from left to right and using James Tanton’s “Exploding Dots” idea.
The article discusses alternative number systems where 0.999… and 1.000… could be treated as different objects, but argues that the standard real number system “glues” these representations together because it gives a more universal and useful structure. It also compares decimal systems with hypothetical alien number systems to show that mathematics aims to describe underlying concepts rather than depend on the symbols we use.
ARTICLE
Summary
The article “More about .999…” explores the mathematical meaning of the infinite decimal 0.999… and why mathematicians consider it exactly equal to 1. The author explains that the difficulty comes from confusing a number with its written representation (a numeral), and shows different ways to understand infinite decimals, including adding them from left to right and using James Tanton’s “Exploding Dots” idea.
The article discusses alternative number systems where 0.999… and 1.000… could be treated as different objects, but argues that the standard real number system “glues” these representations together because it gives a more universal and useful structure. It also compares decimal systems with hypothetical alien number systems to show that mathematics aims to describe underlying concepts rather than depend on the symbols we use.
ARTICLE
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│ KONSTANTINOS MICHAILIDIS │
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│ KONSTANTINOS MICHAILIDIS │
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