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(in which, after five initial +1 terms, the terms alternate in pairs of +1 and −1 terms – the infinitude of both +1s and −1s allows any finite number of 1s or −1s to be prepended, by Hilbert's paradox of the Grand Hotel) is a permutation of Grandi's series in which each value in the rearranged series corresponds to a value that is at ...
The imaginary unit or unit imaginary number (i) is a mathematical constant that is a solution to the quadratic equation x 2 + 1 = 0. Although there is no real number with this property, i can be used to extend the real numbers to what are called complex numbers, using addition and multiplication. A simple example of the use of i in a complex ...
For instance, for Alcuin's version of the problem, =: a camel can carry 30 measures of grain and can travel one leuca while eating a single measure, where a leuca is a unit of distance roughly equal to 2.3 kilometres (1.4 mi).
The ramified type (τ 1,...,τ m |σ 1,...,σ n) can be modeled as the product of the type (τ 1,...,τ m,σ 1,...,σ n) with the set of sequences of n quantifiers (∀ or ∃) indicating which quantifier should be applied to each variable σ i. (One can vary this slightly by allowing the σs to be quantified in any order, or allowing them to ...
Lamb E. (2014), "Does 1+2+3... Really Equal –1/12?", Scientific American Blogs. ... why 1 + 2 + 3 + ⋯ = −1/12 by Brydon Cais from University of Arizona
Euler's identity asserts that is equal to −1. The expression e i π {\displaystyle e^{i\pi }} is a special case of the expression e z {\displaystyle e^{z}} , where z is any complex number . In general, e z {\displaystyle e^{z}} is defined for complex z by extending one of the definitions of the exponential function from real exponents to ...
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1+1 is a mathematical expression that evaluates to: 2 (number) (in ordinary arithmetic) 1 (number) (in Boolean algebra with a notation where '+' denotes a logical disjunction) 0 (number) (in Boolean algebra with a notation where '+' denotes 'exclusive or' operation, or in a quotient ring of numbers modulo 2)