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Maths Glossary
Algorithm : A fixed process which
if caried out systematically produces a desired result.Thus the "Euclidean
algorithm" is a set of rules which when applied to two
integers produces their common divisor.
Complex Number : A 2 dimensional number comprising
a real and imaginary component of the form A+Bi,where
i is the square root of -1.Such numbers are mapped on
the Argand plane and form a matrix of numbers,the imaginary numbers being
at right angles to the real ones.The conjugate
takes the form a-bi.
Continuum Hypothesis : In Cantorian set
theory,the cardinal number of a set designates its "manyness". The cardinality
of the set of integers 1,2,3,... is
designated by
À0.The
cardinality of the set of real numbers is
2À0.The continuum
hyopothesis asserts that there is no set whose cardinal falls between
À0
and
2À0.
Cube : 1. A number raised to the power 3,ie 2 x
2 x 2 = 23 = 8
2. A 3 dimensional figure with
the height,width and depth having the same lengths,and all at right-angles
to each other.
Denominator : The lower number in a
fraction, Numerator/ Denominator.
Diophantine Equation : An equation which
is required to be solved by integers.Thus
the diophantine equation 2x2 - 3y2 =
5 has the integer solution x=2,y=1.
Eigen (value or state) : Possible values for a
parameter of an equation for which the solutions will be compatible with
the boundary conditions.In quantum mechanics the energy eigenvalues for the
Schrödinger equation are the possible energy levels for the system.
Factor: A number that divides into another number.EG
3 and 2 are factors of 6.
Fermat's theorem : The statement
that the equation xn + yn =
xn has no positive integer solution
x,y,z if n is an
integer greater than 2.Fermat's last
problem is currently one of the most famous of the
unsolved problems.
Four Colour Theorem : It is desired to colour
a political map on a plane so that countries sharing a common boundary are
coloured differently. Experience of map-makers has shown that four colours
suffice.This assertion in its precise formulation was an unsolved problem
in mathematics for over a hundred years.It has now been
"proved" by an assist from a computer.
Fraction : A number made up of two numbers,a
numerator and
denominator,the former divided by the latter.
Imaginary Number : A number forming the latter
component of a complex number of the form A+Bi,where
i is the square root of -1.
Integer : The positive integers are 1,2,3,,...The
negative integers are -1,-2,-3...Then there is 0 ,the zero integer. Numbers
with no fractional part.
Irrational Number : A number which cannot
be represented in fractional form,such as PI (3.14159..).
Numerator : The top number of a
fraction,Numerator/ Denominator
Perfect Number : A number that is the sum of
its factors.EG 6=1+2+3
Prime
Number : A number that is only divisible by 1 and itself.
Pythagoras Theorem : The Square on the
Hypotenuse is equal to the sum of the squares of the other to
sides.[H2=Ö(a2 +
b2) ]
Rational Number : A number that is capable
of being represented as a fraction,via
a numerator and
denominator.
Real Number : Any of the
conventional numbers,including
fractions
and irrationals.
Reciprocal : A number that is made into a
fraction.The reciprocal of 2 is 1/2.
Root : The Nth root of a number,is that which when
multiplied by itself N times produces the desired number.The square (2nd)
root of 4 is 2 (2 x 2 = 4).The cube (3rd) root of 27 is 9 (3 x 3 x 3 =9).
Russell's Paradox : Popularly : The Cretan
who said that all Cretan's are liars - is a liar - was he lying or telling
the truth?
In a mathematical context : the set of all sets that are not members of
themselves.This concept embodies a contradiction.
Square : 1. A number raised to the power 2,ie
2 x 2 = 22 = 4
2. A 2 dimensional
figure with the height and width having the same lengths,and at right angles
to each other.
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