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0.999... and 1 + 2 + 4 + 8 + ⋯

Shortcuts: Differences, Similarities, Jaccard Similarity Coefficient, References.

Difference between 0.999... and 1 + 2 + 4 + 8 + ⋯

0.999... vs. 1 + 2 + 4 + 8 + ⋯

In mathematics, 0.999... (also written as 0., 0., or 0.(9)) denotes the smallest number greater than every number in the sequence. In mathematics, is the infinite series whose terms are the successive powers of two.

Similarities between 0.999... and 1 + 2 + 4 + 8 + ⋯

0.999... and 1 + 2 + 4 + 8 + ⋯ have 8 things in common (in Unionpedia): Geometric series, Integer, Leonhard Euler, Mathematical proof, Mathematics, P-adic number, Real number, Series (mathematics).

Geometric series

In mathematics, a geometric series is the sum of an infinite number of terms that have a constant ratio between successive terms.

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Integer

An integer is the number zero (0), a positive natural number (1, 2, 3,...), or the negation of a positive natural number (−1, −2, −3,...). The negations or additive inverses of the positive natural numbers are referred to as negative integers.

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Leonhard Euler

Leonhard Euler (15 April 170718 September 1783) was a Swiss mathematician, physicist, astronomer, geographer, logician, and engineer who founded the studies of graph theory and topology and made pioneering and influential discoveries in many other branches of mathematics such as analytic number theory, complex analysis, and infinitesimal calculus.

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Mathematical proof

A mathematical proof is a deductive argument for a mathematical statement, showing that the stated assumptions logically guarantee the conclusion.

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Mathematics

Mathematics is a field of study that discovers and organizes abstract objects, methods, theories and theorems that are developed and proved for the needs of empirical sciences and mathematics itself.

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P-adic number

In number theory, given a prime number, the -adic numbers form an extension of the rational numbers which is distinct from the real numbers, though with some similar properties; -adic numbers can be written in a form similar to (possibly infinite) decimals, but with digits based on a prime number rather than ten, and extending to the left rather than to the right.

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Real number

In mathematics, a real number is a number that can be used to measure a continuous one-dimensional quantity such as a distance, duration or temperature.

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Series (mathematics)

In mathematics, a series is, roughly speaking, the operation of adding infinitely many quantities, one after the other, to a given starting quantity.

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The list above answers the following questions

0.999... and 1 + 2 + 4 + 8 + ⋯ Comparison

0.999... has 147 relations, while 1 + 2 + 4 + 8 + ⋯ has 31. As they have in common 8, the Jaccard index is 4.49% = 8 / (147 + 31).

References

This article shows the relationship between 0.999... and 1 + 2 + 4 + 8 + ⋯. To access each article from which the information was extracted, please visit: