Discrete Mathematics

218 DISCRETE

MATHEMATICS'---------------------------

which

1ok-l

s;

2'oo

<

wk

Now we can also write 2

100

in the form 1

Ox;

only x will not be an integer: the appropriate value

of

x is

x

= lg 2

100

= 100 lg2. We then have

k-l$x<k,

which means that k - 1 is the largest integer not exceeding

x.

Mathematicians have a name for this: it is the

integer part

or

floor

of

x,

and it is denoted by L x

J.

We can also say that we obtain k by rounding x down to the

next integer. There is also a name

for the number obtained by rounding x up to the next integer: it is called the

ceiling

of

x, and denoted by I x

l·

Using

any

scientific

calculator

(or table

of ...