Big
Calculator
Perform calculations with results up to 10000 figures. Investigate repeating decimal patterns of fractions. Look at the decimal form of irrational numbers. See description of method for calculating pi.
|
Real numbers |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
The set R of real numbers is represented by the points on the number line. The hierarchy of numbers shows the natural numbers N as a subset of the whole numbers W, which is a subset of the integers Z, which is a subset of the rational numbers Q, which is a subset of the real numbers R. The set of irrational numbers Q' consists of those real numbers that are not rational.
The real numbers are a field i.e. the operations of addition and multiplication obey the closure, commutative, associative, identity, inverse and distributive properties.
Irrational numbers have a decimal form that is infinite and non repeating. Rational numbers have a decimal form that either terminates or repeats. Irrational numbers are often expressed as the limit of an infinite sequence or the sum of an infinite series.
Irrational numbers consist of surds (e.g. square root of 2) and transcendental numbers (e.g. pi). The study of surds involves simplifying, rationalising the denominator and arithmetic.
Inequalities (including those involving absolute value) can be solved both graphically and analytically. The absolute value of a real number is defined as its distance from 0.
Big
Calculator
Perform calculations with results
up to 10000 figures. Investigate repeating decimal patterns of fractions.
Look at the decimal form of irrational numbers. See description of method
for calculating pi.
Integers,
rational & irrational numbers - Math Forum
Zero
in Four Dimensions: Cultural, Historical, Mathematical, and Psychological
Perspectives - Professor Hossein Arsham
In the 13th century, the introduction
of zero was crucial to the development of the decimal system.
History
of zero - MacTutor History Archive
Egyptian
fraction calculator
The ancient Egyptians represented
all fractions as a sum of unit fractions (3/4 would have been written as
1/2+1/4). 1/7+1/7 is not allowed for 2/7 as the same unit fraction cannot
be used twice (the calculator gives 1/4+1/28).
continued
fractions
introduction, history, applications
and resources
Square
root of 2 is irrational - proof by contradiction.
Square
root of 3 is irrational - proof by contradiction.
one
million digits of the square roots of 2,3,5,6,7,8,10
History
of e - MacTutor History Archive
e
is irrational - proof by contradiction
Numbers,
Constants and Computation
Inequalities
- SOS MAthematics Algebra
Earliest
Uses of Symbols in Mathematics
Earliest
Uses of Words in Mathematics
Nature
of Infinity - Michigan Maths Scholars
0.999... = 1 ?
"Our minds are finite, and yet even
in these circumstances of finitude we are surrounded by possibilities that
are infinite, and the purpose of life is to grasp as much as we can out
of that infinitude."
Alfred North Whitehead (1861 - 1947)