atestado$1$ - translation to English
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atestado$1$ - translation to English

DIVERGENT SERIES
1+1+1+···; 1 + 1 + 1 + 1 + 1 + · · ·; 1 + 1 + 1 + 1 + · · ·; 1 + 1 + 1 + 1 + …; 1 + 1 + 1 + 1 + ...; Zeta(0)
  • alt=A graph showing a line that dips just below the ''y''-axis

atestado 1      
n. attestation, testimony under oath
number one         
  • The 24-hour tower clock in [[Venice]], using ''J'' as a symbol for 1
  • [[Hoefler Text]], a typeface designed in 1991, represents the numeral 1 as similar to a small-caps I.
  • alt=Horizontal guidelines with a one fitting within lines, a four extending below guideline, and an eight poking above guideline
  • 1 as a resin identification code, used in recycling
  • This Woodstock typewriter from the 1940s lacks a separate key for the numeral 1.
NATURAL NUMBER
1 (the number); ¹; One (number); 1 E0; One; Unity (number); ₁; ١; ۱; Number one; ១; 1.0; No 1; 1; NO.1; ➊; ➀; ❶; Unity (mathematics); The number one; 𐡘; ꩑; ༡; 1 (numeral); One (1); Number-one; Numberone; ௧; १; ১; ੧; No.1; ૧; ୧; ౧; ೧; ൧; ߁; ໑; ၁; ႑; ꧑; ᥇; 𐒡; ꣑; 1 (glyph); Firstly; Nº 1; Unit number; 1e0; 1E0; 1 (number); 1️⃣; 10^0; Unit (number); ASCII 49; \x31; 2^0; U+0031; User talk:Theonlysameer/sandbox; 1024^0; 1×2^0; 1B0; 1×10^0; 1000^0; 100^0; 1^1; 1^0; 1⁰; 1¹; 1**0; 1**1; 2⁰; 2**0; 1²; 1³; 1⁴; 1⁵; 1⁶; 1⁷; 1⁸; 1⁹; 1¹⁰; 1^2; 1^3; 1^4; 1^5; 1^6; 1^7; 1^8; 1^9; 1^10; 1**2; 1**3; 1**4; 1**5; 1**6; 1**7; 1**8; 1**9; 1**10; 10⁰; 10**0; 1000⁰; 1000**0; 1 B0; 1024⁰; 1024**0
(adj.) = número uno, líder, principal
Ex: Eyestrain is the number one complaint of computer users.
one         
  • The 24-hour tower clock in [[Venice]], using ''J'' as a symbol for 1
  • [[Hoefler Text]], a typeface designed in 1991, represents the numeral 1 as similar to a small-caps I.
  • alt=Horizontal guidelines with a one fitting within lines, a four extending below guideline, and an eight poking above guideline
  • 1 as a resin identification code, used in recycling
  • This Woodstock typewriter from the 1940s lacks a separate key for the numeral 1.
NATURAL NUMBER
1 (the number); ¹; One (number); 1 E0; One; Unity (number); ₁; ١; ۱; Number one; ១; 1.0; No 1; 1; NO.1; ➊; ➀; ❶; Unity (mathematics); The number one; 𐡘; ꩑; ༡; 1 (numeral); One (1); Number-one; Numberone; ௧; १; ১; ੧; No.1; ૧; ୧; ౧; ೧; ൧; ߁; ໑; ၁; ႑; ꧑; ᥇; 𐒡; ꣑; 1 (glyph); Firstly; Nº 1; Unit number; 1e0; 1E0; 1 (number); 1️⃣; 10^0; Unit (number); ASCII 49; \x31; 2^0; U+0031; User talk:Theonlysameer/sandbox; 1024^0; 1×2^0; 1B0; 1×10^0; 1000^0; 100^0; 1^1; 1^0; 1⁰; 1¹; 1**0; 1**1; 2⁰; 2**0; 1²; 1³; 1⁴; 1⁵; 1⁶; 1⁷; 1⁸; 1⁹; 1¹⁰; 1^2; 1^3; 1^4; 1^5; 1^6; 1^7; 1^8; 1^9; 1^10; 1**2; 1**3; 1**4; 1**5; 1**6; 1**7; 1**8; 1**9; 1**10; 10⁰; 10**0; 1000⁰; 1000**0; 1 B0; 1024⁰; 1024**0
uno

Definition

Enfermedad de AUJESZKY
pseudorabia producida por un virus del género Herpesvirus [ICD-10: B33.8]

Wikipedia

1 + 1 + 1 + 1 + ⋯

In mathematics, 1 + 1 + 1 + 1 + ⋯, also written n = 1 n 0 {\displaystyle \sum _{n=1}^{\infty }n^{0}} , n = 1 1 n {\displaystyle \sum _{n=1}^{\infty }1^{n}} , or simply n = 1 1 {\displaystyle \sum _{n=1}^{\infty }1} , is a divergent series, meaning that its sequence of partial sums does not converge to a limit in the real numbers. The sequence 1n can be thought of as a geometric series with the common ratio 1. Unlike other geometric series with rational ratio (except −1), it converges in neither the real numbers nor in the p-adic numbers for some p. In the context of the extended real number line

n = 1 1 = + , {\displaystyle \sum _{n=1}^{\infty }1=+\infty \,,}

since its sequence of partial sums increases monotonically without bound.

Where the sum of n0 occurs in physical applications, it may sometimes be interpreted by zeta function regularization, as the value at s = 0 of the Riemann zeta function:

ζ ( s ) = n = 1 1 n s = 1 1 2 1 s n = 1 ( 1 ) n + 1 n s . {\displaystyle \zeta (s)=\sum _{n=1}^{\infty }{\frac {1}{n^{s}}}={\frac {1}{1-2^{1-s}}}\sum _{n=1}^{\infty }{\frac {(-1)^{n+1}}{n^{s}}}\,.}

The two formulas given above are not valid at zero however, but the analytic continuation is.

ζ ( s ) = 2 s π s 1   sin ( π s 2 )   Γ ( 1 s )   ζ ( 1 s ) , {\displaystyle \zeta (s)=2^{s}\pi ^{s-1}\ \sin \left({\frac {\pi s}{2}}\right)\ \Gamma (1-s)\ \zeta (1-s)\!,}

Using this one gets (given that Γ(1) = 1),

ζ ( 0 ) = 1 π lim s 0   sin ( π s 2 )   ζ ( 1 s ) = 1 π lim s 0   ( π s 2 π 3 s 3 48 + . . . )   ( 1 s + . . . ) = 1 2 {\displaystyle \zeta (0)={\frac {1}{\pi }}\lim _{s\rightarrow 0}\ \sin \left({\frac {\pi s}{2}}\right)\ \zeta (1-s)={\frac {1}{\pi }}\lim _{s\rightarrow 0}\ \left({\frac {\pi s}{2}}-{\frac {\pi ^{3}s^{3}}{48}}+...\right)\ \left(-{\frac {1}{s}}+...\right)=-{\frac {1}{2}}}

where the power series expansion for ζ(s) about s = 1 follows because ζ(s) has a simple pole of residue one there. In this sense 1 + 1 + 1 + 1 + ⋯ = ζ(0) = −1/2.

Emilio Elizalde presents a comment from others about the series:

In a short period of less than a year, two distinguished physicists, A. Slavnov and F. Yndurain, gave seminars in Barcelona, about different subjects. It was remarkable that, in both presentations, at some point the speaker addressed the audience with these words: 'As everybody knows, 1 + 1 + 1 + ⋯ = −1/2.' Implying maybe: If you do not know this, it is no use to continue listening.