Group:
philosophy of mathematics
Topic:
boolean values, binary numbers, and bit strings
Topic:
constants
Topic:
enumerated data types
Topic:
FOCUS number system
Topic:
infinity and infinitesimal
Topic:
integer values and operations
Topic:
number as a named set of numbers
Topic:
number representation
Topic:
primitive data types of a language
Topic:
random number generation
Topic:
real numbers and floating point numbers
Topic:
representation data type
Topic:
unbounded precision
Topic:
undefined, null, and other signal values
Topic:
units
Topic:
what is a number
| |
Subtopic: number theory 
| Quote: Euclid's algorithm for greatest common divisor; with proof [»eucl_300, OK]
|
Subtopic: number types
| Quote: different types of numbers do not include simpler types; e.g., the positive integers are not the same as the natural numbers [»russB_1919, OK]
| | Quote: the positive and negative integers are relations instead of a class of classes; e.g., -n is the relation of n to n+m [»russB_1919, OK]
| | Quote: the fraction m/n is the relation that holds of inductive numbers x,y when xn=ym; leads to ordering relation on fractions [»russB_1919, OK]
|
Subtopic: huge numbers
| Quote: India used immense numbers from ancient times; for example, the Hindus used 18 denominations and in the Lalitavistara, tallaksana is 10^53 [»dattB_1935]
| | Quote: some of the numbers named by Archimedes exceed the grains of sand that would fill the universe [»arch_287]
|
Subtopic: decimal number system
| Quote: ten has always been the basis of numeration in India [»dattB_1935]
| | Quote: the decimal number system appears to be of Hindu origin sometime before 595 A.D.; only India switched from the old system to the new one using the same numerical signs [»dattB_1935]
| | Quote: any number can be written with the nine digits from India and zero from Arabic [»leon_1202]
|
Subtopic: zero
| Quote: the earliest known use of the zero symbol is by Pingala (before 200 B.C.) [»dattB_1935]
| | Quote: the Hindus define zero as the result of a-a [»dattB_1935]
| | Quote: Bhaskara II (1150): in a/0 there is no alteration, as no change takes place in the infinite and immutable God [»dattB_1935]
|
Subtopic: imaginary numbers
| Quote: the imaginary number i is the solution to the self-referential equation x=-1/x [»browGS_1972, OK]
|
Subtopic: computable numbers
| Quote: the computable numbers are the real numbers whose decimal expression can be calculable by finite means; because human memory is limited [»turiAM11_1936]
|
Subtopic: Godel number
| Quote: a Godel number is a name for a string [»hofsDR_1979, OK]
|
Subtopic: natural number
| Quote: the natural numbers are the posterity of 0 w.r.t. immediate predecessor; i.e., all larger numbers, by hereditary; includes Peano's 0 and induction [»russB_1919, OK]
| | Quote: we define the natural numbers as those to which proofs by mathematical induction can be applied
| | Quote: the sole natural object of mathematical thought is the whole number [»poinH_1905, OK]
|
Subtopic: rational numbers
| Quote: the fraction m/n is the relation that holds of inductive numbers x,y when xn=ym; leads to ordering relation on fractions [»russB_1919, OK]
| | Quote: every rational and irrational number is symbol for a cut that divides the real numbers into two
|
Subtopic: irrational number
| Quote: rational and irrational as commensable or incommensurable magnitudes [»eucl_300, OK]
| | Quote: solve algebraic equations by generalization of addition by iteration: get negative numbers and reciprocal powers from subtraction, fractions from division, irrationals from fractional powers, and complex numbers from the square root of -1 [»feynRP_1963]
| | Quote: the square root of 2 is the cut between numbers whose square is less than and greater than 2; Kronecker [»poinH_1902, OK]
|
Subtopic: prime number
Quote: prime number as measured by unit alone; composite numbers as relatively prime
|
Related Topics
Group: philosophy of mathematics (11 topics, 330 quotes)
Topic: boolean values, binary numbers, and bit strings (44 items)
Topic: constants (21 items)
Topic: enumerated data types (17 items)
Topic: FOCUS number system (8 items)
Topic: infinity and infinitesimal (37 items)
Topic: integer values and operations (13 items)
Topic: number as a named set of numbers (15 items)
Topic: number representation (16 items)
Topic: primitive data types of a language (31 items)
Topic: random number generation (29 items)
Topic: real numbers and floating point numbers (37 items)
Topic: representation data type (21 items)
Topic: unbounded precision (9 items)
Topic: undefined, null, and other signal values (34 items)
Topic: units (23 items)
Topic: what is a number
(55 items)
|
