σύντομος$1$ - translation to
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σύντομος$1$ - translation to

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

compact flash         
  • Pins of a CFast card
  • 1 GB CF card in a [[Nikon D200]] [[DSLR]] camera
  • Various CF I/O [[network interface card]]s
  • A 16-GB CompactFlash card installed in a 2.5" IDE port with adapter
  • CompactFlash to [[SATA]] adapter with a card inserted
  • IBM 1 GB Microdrive
FLASH MEMORY MASS STORAGE DEVICE
CompactFlash I; CompactFlash II; Compact Flash; Compact flash; Compactflash; Compact-flash; Compact-Flash; CF card; CF2; CompactFlash card; Cf card; CF1; CF-I; CF-II; CompactFlash Card; CFast; CF Card; CompactFlash Association; CF (memory card); CFast 1.0; CFast 2.0; CF-2
compact flash
news editor         
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WORK THAT AN EDITOR DOES TO IMPROVE THE FORMATTING, STYLE, AND ACCURACY OF TEXT
Copyediting; Copy-editing; Copy editor; Copyedit; Copy edit; Copy-edit; Copyeditor; Copy editors; Copy desk; Sub-editing; Copy Editing; Deskman; Cped; Copy-editor; Sub-editor; Subeditor; Copy chief; Copy Editor; Business editing; Copy edited; Assistant editor; Subediting; Copyeditors; Copyedits; Supervising editor; Copy desk chief; News editor; Sub (editor); Chief subeditor; Chief sub-editor; Mechanical copy editing; Substantive copy editing; Light copy editing; Medium copy editing; Heavy copy editing; Mechanical editing; C/e; Copyreader
συντάκτης ειδήσεων
Chief Executive         
HIGHEST-RANKING CORPORATE OFFICER
CEO; Chief Executive Officer; Chief executive; Corporate executive officer; Chief Executive; Managing Director; Managing director; Chief Executive Office; C.E.O.; Ceo; Chief executive officers; CEOs; Senior managing director; Senior Managing Director; Chief executives; Cheif executive officer; Chief Executive Officers; Managing directors; Chairman & CEO; Administrating director; Co-chief executive officer; Group Chief Executive; Group CEO; Group Chief Executive Officer; C.E.O; Group Managing Director; CEO (chief executive officer); Group Chief executive officer; Chief executive office; Group chief executive officer; Chief Exec; Co-Chief executive officer; Chief Exec.; Chief Executive Officer (corporate title)
n. γενικός διευθυντής

Definition

CF
¦ abbreviation
1. (in the UK) Chaplain to the Forces.
2. cystic fibrosis.

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.