1549901369-Elements_of_Real_Analysis__Denlinger_

722 Glossary of Symbols

Symbol

{xn}

lim Xn = L

n->oc

Xn---+ L

Tm

SEQUENCES

Meaning

a sequence of real numbers

The sequence {xn} has limit L.

The sequence {xn} converges to L.

m-tail of a sequence {xn}

Defined on page

50

52

lim Xn = ±oo The sequence {xn} has limit + oo or - oo.

52

69

82

n->oc

Xn---+ ±oo The sequence {xn} diverges to + oo or - oo.^82

lim Xn, lim Xn lower and upper limits of {xn}

n->oc n->oc

TOPOLOGY OF JR

Symbol Meaning

NE(x) 1::-neighborhood of x

Ao, Aext, Ab interior, exterior, and boundary of A

A, Ac1 closure of A

A' set of all cluster points of A

d(A) diameter of A

μ(A) measure of A

M class of all μ-measurable sets

LIMITS OF FUNCTIONS

Symbol Meaning

lim f(x) = L f has limit Las x approaches xo.

deleted 1::-neighborhoocl of Xo

X-+Xo

N~(xo)

131, 132

Defined on page

138

141 -143

149

150

163

171

171

Defined on page

178

188

lim f(x) or f(xci)

x-+x{j

limit of f as x approaches xo from the right 203 , 237

lim f(x) or f(x 0 )

x-+xQ

lim f(x) = +oo

X-+Xo

lim f(x) = - oo

X-tXo

lim f(x) = L

x->+oc

X-+-00 lim f(x) = L

limit of f as x approaches x 0 from the left 203 , 237

f has limit + oo as x approaches x 0.

f has limit - oo as x approaches x 0.

f has limit L as x approaches + oo.

f has limit L as x approaches - oo.

209

209

217

217