Integers in Python:

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What is an Integer?

In Mathematics:

An integer is a number that has no fractional[1] component.  The term ‘integer’ in Latin means ‘whole.’  So an Integer is a Whole Number[2].  A person who practises wholesome behaviour is a person with integrity.

In Number Theory, the set of integers is very often represented by a boldface Capital ‘Z’[3]:

Z

Sometimes, in Number Theory, the set of integers is represented by a blackboard bold ‘Z’:

 

The set of integers comprises:

• the number:

0

• the sequence of positive Natural Numbers:

{1, 2, 3, 4, 5…}

• the sequence of negative integers:

{-1, -2, -3, -4, -5…}

In Python:

In Python, integers are a datatype.  This datatype is assigned the keyword:

int

Figure 1:  In Python, the int keyword represents the integer datatype.

In Python, we can use the:

int()

method so as to convert numbers that might exist as strings, or other datatypes, to integers:

Figure 2:  In the above example, we convert the number, 3, from a Python string to a Python integer by using the int() method.  This is called ‘type conversion.’

Figure 3:  In the above example, we convert the number, 3.0, from a Python float to a Python integer by using the int() method.  This is called ‘type conversion.’

Glossary:

integer

• noun.
  1. a number which is not a fraction; a whole number.
  2. a thing complete in itself.

<ORIGIN early 16^th century (as an adjective meaning ‘entire, whole’): from Latin, ‘intact, whole’, from in– (expressing negation) + the root of tangere ‘to touch’.  Compare with ENTIRE, also with Integral, integrate, and INTEGRITY[4].

<ETYMOLOGY> From the Latin 1^st-and-2^nd-declension adjective, ‘integra, integer, integrum,’ which means ‘complete,’ ‘whole,’ ‘intact.’  From the Latin prefix ‘in-,’ which expresses negation; and the Latin verb ‘tangō, tangere, tetigī, tāctum,’ which means ‘to touch.’  Etymologically, therefore, an ‘integer’ is a number that is ‘intact’ i.e. which does not have a fractional component.

 

 

 

 

 

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[1]  Whereas ‘integer’ comes from the Latin word for ‘whole,’ ‘fraction’ comes from the Latin supine ‘frāctum,’ which means ‘broken.’  The term ‘fraction’ is derived from the Latin 3^rd-conjugation verb, frangō, frangere, frēgī, frāctum,’ which means ‘to break,’ ‘to shatter.’  If something be fragile, then it is easily broken; it is liable to shatter.  A fraction, etymologically, is like a broken-off piece of a number.

[2]  I speak, here, in general parlance.  Mathematically, some would argue a difference between whole numbers and integers.  Mathematicians sometimes regard whole numbers as comprising the sequence of positive integers: {0, 1, 2, 3, 4, 5…}.  I am merely trying to get across the concept that an Integer has no fractional part.

[3]  The ‘Z’ represents the plural of the German feminine noun, ‘die Zahl,’ ‘the number,’ which is ‘die Zahlen.’

[4]  Oxford University Press. Oxford Dictionary of English (Electronic Edition). Oxford. 2010.  Loc 357261