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– identically equal,
– approximately equal,
~ – approximately,
0.(12345) – the repeating decimal with the period 12345,
N – the set of natural numbers,
Z – the set of whole numbers (integers),
R – the set of real numbers,
Ø – an empty set,
– an infinity sign,
– an element x belongs to a set X,
– a union of sets X and Y,
– an intersection of sets X and Y,
{ un } – a sequence with a general term un ,
[ a, b ] – a numerical segment,
– numerical semi-segments (semi-intervals),
(a, b) – a numerical interval,
– a scalar product of vectors 
,
– a vector product of vectors 
,
==> – it follows,
<=> – equivalent,
– perpendicular,
– parallel,
– a triangle ABC,
– a function and its derivative
Solutions to problems:
Problem 1: Across the river
In Fig. 4.1, the man has adjusted the brim of his hat so that his eyes just see past the brim of the hat to the distant point X on the other bank of the river. With the ground, this forms a triangle whose shape is fixed by angle at which the brim of his hat is tipped. By turning his head, and looking past the brim of his hat to a point on the ground which is on his side of the river, he will be identifying a point he can reach on foot, which is the required distance away – and all he has to do is pace out the distance.
Fig. 4.1
Problem 2: Three men in the hotel
The three men paid only $25 for the room, not $27; the bellboy returned $3 to them and kept the other $2 for himself. Therefore: $25 + $3 + $2 = $30
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Problem 3: Practice questions
1) 12/13 2) 0.15 3) a) 1/16 b) 1/169 c) 100/169 4) a) 1/2 b) 1/2 c) 1/4
Content
Стр.
От составителя 3
Unit I. Triangles 4
Unit II. Prime Numbers 12
Unit III. Game Theory 17
Supplement 29
Bibliography 34
