drummyfish/less_retarded_wiki
5
1
Fork 0
Code Issues Pull requests Projects Releases Packages Wiki Activity

Update

Browse source
This commit is contained in:
Miloslav Ciz 2024-05-19 22:21:45 +02:00
parent 1bdfbe36f8
commit e94761138d
14 changed files with 1778 additions and 1768 deletions
Download patch file Download diff file Expand all files Collapse all files

4
number.md
View file

@ -10,13 +10,13 @@ Let's not [confuse](often_confused.md) numbers with digits or figures (numerals)
Humans first started to use positive natural numbers (it seems as early as 30000 BC), i.e. 1, 2, 3 ..., so as to be able to trade, count enemies, days and so on -- since then they kept expanding the concept of a number with more [abstraction](abstraction.md) as they encountered more complex problems. First extension was to fractions, initially reciprocals of integers (like one half, one third, ...) and then general ones. Around 6th century BC Pythagoras showed that there even exist numbers that cannot be expressed as fractions ([irrational numbers](irrational_number.md), which in the beginning was a controversial discovery), expanding the set of known numbers further. A bit later (around 100 BC) negative numbers started to be used. Adoption of the number [zero](zero.md) also took some time (1st use of true zero seem to be in 4th century BC), with it first just having a limited use as a mere placeholder digit. Since 16th century a highly abstract concept of [complex numbers](complex_number.md) started to appear, which was later (19th century) expanded further to [quaternions](quaternion.md). With more advancement in mathematics -- e.g. with the development of set theory -- more and more concepts of new kinds of numbers appeared and still appear to this day. Nowadays we have greatly abstract numbers, ones existing in many dimensions, capable of counting and measuring infinitely large and infinitely small entities, and it seems we still haven't nearly discovered everything there is to know about numbers.
Basically **anything can be encoded as a number** which makes numbers a universal abstract "medium" -- we can exploit this in both mathematics and programming. Ways of encoding [information](information.md) in numbers may vary, for a mathematician it is natural to see any number as a multiset of its [prime](prime.md) factors (e.g. 12 = 2 * 2 * 3, the three numbers are inherently embedded within number 12) that may carry a message, a programmer will probably rather encode the message in [binary](binary.md) and then interpret the 1s and 0s as a number in direct representation, i.e. he will embed the information in the digits. You can probably come up with many more ways.
Basically **anything can be encoded as a number** which makes numbers a universal abstract "medium" -- we can exploit this in both mathematics and programming (which are actually the same thing). Ways of encoding [information](information.md) in numbers may vary, for a mathematician it is natural to see any number as a multiset of its [prime](prime.md) factors (e.g. 12 = 2 * 2 * 3, the three numbers are inherently embedded within number 12) that may carry a message, a programmer will probably rather encode the message in [binary](binary.md) and then interpret the 1s and 0s as a number in direct representation, i.e. he will embed the information in the digits. You can probably come up with many more ways.
**[Order](order.md)** is an important concept related to numbers, we usually want to be able to compare numbers so apart from other operations such as addition and multiplication we also define the comparison operation. However note that not every order is total, i.e. some numbers may be incomparable (consider e.g. complex numbers).
Here are some [fun](fun.md) facts about numbers:
- Some people associate numbers with colors, though what color each number has seems to be completely subjective. See [synesthesia](synesthesia.md).
- Some people associate numbers with [colors](color.md), though what color each number has seems to be completely subjective. See [synesthesia](synesthesia.md).
- There is a funny hypothetical number between 6 and 7 called [thrembo](thrembo.md).
- There exist [illegal numbers](illegal_number.md), owing to the above mentioned fact that any information can be encoded as a number along with the fact that some information is illegal (see e.g. "[intellectual property](intellectual_property.md)").
- ...