m (Expanding) |
(Your explanation is incorrect. The empty string is valid expression, it is stated that the array can be I<>. And that expression is also not ill-defined, since I had the foresight to put "I<> = 0".) Tag: Source edit |
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'''Infra notation''' is a notation for large numbers made by Wikia user [[User:Nirvana Supermind|Nirvana Supermind]].<ref>{{cite web|last=Nirvana Supermind|url=https://integralview.wordpress.com/2020/12/08/infra-notation/|title=Infra Notation - Integral View}}</ref>. |
'''Infra notation''' is a notation for large numbers made by Wikia user [[User:Nirvana Supermind|Nirvana Supermind]].<ref>{{cite web|last=Nirvana Supermind|url=https://integralview.wordpress.com/2020/12/08/infra-notation/|title=Infra Notation - Integral View}}</ref>. |
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The notation is currently composed of 1 parts, which is as follows: |
The notation is currently composed of 1 parts, which is as follows: |
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− | * [https://integralview.wordpress.com/2020/12/08/basic-infra-notation/ Basic Infra Notation] (BIN)<ref>{{cite web||last=Nirvana Supermind|url=https://integralview.wordpress.com/2020/12/08/basic-infra-notation/|title=Basic Infra Notation - Integral View |
+ | * [https://integralview.wordpress.com/2020/12/08/basic-infra-notation/ Basic Infra Notation] (BIN)<ref>{{cite web||last=Nirvana Supermind|url=https://integralview.wordpress.com/2020/12/08/basic-infra-notation/|title=Basic Infra Notation - Integral View}} </ref>. |

− | It is notable that the creator always insists that something like "The notation is currently composed of 1 parts" whenever he or she started to make a new notation, it does not mean that he or she will expand it. Indeed, the creator invented [[Rampant Array Notation]], [[Extensible Illion System]], and [[Quick array notation]], but none of them has been completed. |
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== Basic notation == |
== Basic notation == |
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− | Basic Infra Notation (BIN) is the 1st part of Infra Notation. It’s the simplest and weakest one. |
+ | Basic Infra Notation (BIN) is the 1st part of Infra Notation. It’s the simplest and weakest one. The rules for it are: |

− | |||

− | === Original definition === |
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− | A valid expression in this notation is of the form I<>, I<a>, or I<a,b> for non-negative integers a and b. The rules for a valid expression are: |
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# I<> = 0 |
# I<> = 0 |
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Where # is a part of said array (a string of entries and commas, it can also be empty). If there are two or more distinct rules to apply to a single expression, the uppermost-numbered rule which is applicable and whose result is a valid expression will be applied. The creator said that this notation most likely reaches f<sub>ω</sub>(n) in the [[Fast-growing hierarchy]]. |
Where # is a part of said array (a string of entries and commas, it can also be empty). If there are two or more distinct rules to apply to a single expression, the uppermost-numbered rule which is applicable and whose result is a valid expression will be applied. The creator said that this notation most likely reaches f<sub>ω</sub>(n) in the [[Fast-growing hierarchy]]. |
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− | Note that the creator always insists something like '''"this notation is well-defined"''' or '''"this notation most likely reaches blah-blah"''', but those statements are not necessarily true. Indeed, none of them was well-defined when the creator created the corresponding article in this wiki. Unfortunately, this notation is not a counterexample, as I<0,1> is ill-defined because there is no rule applied to it. The first three rules are not applicable to it. The fourth rule is applicable to it, but the resulting expression is the empty string, which is not a valid expression in this notation. Namely, this notation is ill-defined, if we consider the issue. The creator tends to insists that any error pointed by others can be regarded as a typo, and hence does not contribute to the ill-definedness. If one stands on the creator's viewpoint that any error is a typo which does not contribute to the ill-definedness, then it might be regarded as a well-defined notation whose computation rule is uniquely applicable to any valid expression. |
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=== Example === |
=== Example === |
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= 10<sup>10<sup>1000</sup></sup> |
= 10<sup>10<sup>1000</sup></sup> |
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− | I<0,1> = ill-defined |
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− | |||

− | === Alternative definition === |
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− | It is quite elementary to fix the issue. For example, we define a non-negative integer I<@> for any array @ of non-negative integers in the following recursive way: |
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− | # If @ is the empty string, then I<@> = 0. |
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− | # If @ = "a" for a non-negative integer a, then I<@> = 10<sup>a</sup>. |
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− | # If @ = "#,0" for a non-empty array # of non-negative integers, then I<@> = I<#>. |
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− | # If @ = "#,a,b" for an array # of non-negative integers, non-negative integer a, and a positive integer b, then I<@> = I<sup>a</sup><#,a,b-1>, where I<sup>n</sup><#,a,b-1> is the non-negative integer defined for any non-negative integer n in the following recursive way: |
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− | ## If n = 0, then I<sup>n</sup><#,a,b-1> = a. |
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− | ## If n ≠ 0, then I<sup>n</sup><#,a,b-1> = I<#,I<sup>n-1</sup><#,a,b-1>,b-1>. |
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− | For example, we have I<0,1> = I<sup>0</sup><0,0> = 0. |
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− | == See also == |
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− | * [[Rampant Array Notation]] |
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− | * [[Extensible Illion System]] |
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− | * [[Quick array notation]] |
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== Sources == |
== Sources == |
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<references /> |
<references /> |
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− | [[Category:Numbers by Nirvana Supermind]] |
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[[Category:Notations]] |
[[Category:Notations]] |
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[[Category:Functions]] |
[[Category:Functions]] |
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− | [[Category:Incomplete]] |

## Revision as of 10:29, 9 December 2020

**Infra notation** is a notation for large numbers made by Wikia user Nirvana Supermind.^{[1]}.

The notation is currently composed of 1 parts, which is as follows:

- Basic Infra Notation (BIN)
^{[2]}.

## Basic notation

Basic Infra Notation (BIN) is the 1st part of Infra Notation. It’s the simplest and weakest one. The rules for it are:

- I<> = 0
- I<a> = 10
^{a} - I<#,0> = I<#>
- I<a,b> = I<I<...<I<a,b-1>,b-1>,...>,b-1> (b>0) for a times

Where # is a part of said array (a string of entries and commas, it can also be empty). If there are two or more distinct rules to apply to a single expression, the uppermost-numbered rule which is applicable and whose result is a valid expression will be applied. The creator said that this notation most likely reaches f_{ω}(n) in the Fast-growing hierarchy.

### Example

I<3,1>

= I<I<...<I<3,0>,0>,...>,0> for 3 times

= I<I<I<3,0>,0>,0>

= I<I<I<3>>>

= 10^{101000}

## Sources

- ↑ Nirvana Supermind. Infra Notation - Integral View.
- ↑ Nirvana Supermind. Basic Infra Notation - Integral View.

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