1549901369-Elements_of_Real_Analysis__Denlinger_

Glossary of Symbols 723

CONTINUOUS FUNCTIONS

Symbol Meaning Defined on page

sgn (x) signum function 227

T(x) Thomae's function 229

lxJ greatest integer (floor) function^241

XA(x) characteristic function of (the set) A^244

! IA f restricted to the set A^246

y'X unique nonnegative nth root of x ::'.". 0 253

'P Cantor's function^270 -^273

ax ax for a > 1 and x E IR 280

xt xt for x E IR and t > 0 283

logax loga x for a, x >^0 288

'l/J1(A) oscillation of f on the set A^292

'l/J1(x) oscillation of f at x^292

F 17 -set a union of countably many closed sets 293

DIFFERENTIABLE FUNCTIONS

Symbol Meaning Defined on page

f'(xo) derivative of f at xo^297

f'_(xo), f~(xo) derivative off from the left (right) at xo^302

Dxf(x), d~~), d~f(x) alternative notation for the derivative off 306

I 9:Ji__ d

Y'dx'dxY

j(k)(x)

Tn(x)

Rn(x)

alternative notation for the derivative of f

nth derivative of f at x

nth Taylor polynomial for f

nth Taylor remainder for f

306

329

329 , 519

329,5 19