sxlxc/readableFilter
1
0
Fork 0
Code Issues Pull Requests Actions Packages Projects Releases Wiki Activity

add an example

Browse Source
This commit is contained in:
Yu Cong
2025-10-13 15:20:39 +08:00
parent 2b9c9a7245
commit a3f26f79a7
4 changed files with 7 additions and 4 deletions
Download Patch File Download Diff File Expand all files Collapse all files

92
example/algebraic_structures.processed.md Normal file
View File

@@ -0,0 +1,92 @@
::: {#magma .Definition title="magma"}
A magma is a set M with an operation ⋅ that sends any two elements a, b
∈ M to another element, a⋅b∈M. The symbol ⋅ is a general placeholder for
a properly defined operation. This requirement that for all a, b in M,
the result of the operation a⋅b also be in M, is known as the magma or
closure property.
:::
::::: {#semigroup .Definition title="semigroup"}
To understand semigroup, you need to know magma...
:::: {#incmagma include="magma"}
::: {.Definition title="magma"}
A magma is a set M with an operation ⋅ that sends any two elements a, b
∈ M to another element, a⋅b∈M. The symbol ⋅ is a general placeholder for
a properly defined operation. This requirement that for all a, b in M,
the result of the operation a⋅b also be in M, is known as the magma or
closure property.
:::
::::
... Now you know magma, let's see the definition of semigroup.
(S, ⋅) is a semigroup if it is an associative magma.
:::::
::::::: {#monoid .Definition title="monoid"}
To understand monoid, you need to know semigroup...
:::::: {#incsemigroup include="semigroup"}
::::: {.Definition title="semigroup"}
To understand semigroup, you need to know magma...
:::: {#incmagma include="magma"}
::: {.Definition title="magma"}
A magma is a set M with an operation ⋅ that sends any two elements a, b
∈ M to another element, a⋅b∈M. The symbol ⋅ is a general placeholder for
a properly defined operation. This requirement that for all a, b in M,
the result of the operation a⋅b also be in M, is known as the magma or
closure property.
:::
::::
... Now you know magma, let's see the definition of semigroup.
(S, ⋅) is a semigroup if it is an associative magma.
:::::
::::::
... Now you know semigroup, let's see the definition of monoid.
A monoid is a semigroup with an identity element.
:::::::
::::::::: {#group .Definition title="group"}
To understand group, you need to know monoid...
:::::::: {#incmonoid include="monoid"}
::::::: {.Definition title="monoid"}
To understand monoid, you need to know semigroup...
:::::: {#incsemigroup include="semigroup"}
::::: {.Definition title="semigroup"}
To understand semigroup, you need to know magma...
:::: {#incmagma include="magma"}
::: {.Definition title="magma"}
A magma is a set M with an operation ⋅ that sends any two elements a, b
∈ M to another element, a⋅b∈M. The symbol ⋅ is a general placeholder for
a properly defined operation. This requirement that for all a, b in M,
the result of the operation a⋅b also be in M, is known as the magma or
closure property.
:::
::::
... Now you know magma, let's see the definition of semigroup.
(S, ⋅) is a semigroup if it is an associative magma.
:::::
::::::
... Now you know semigroup, let's see the definition of monoid.
A monoid is a semigroup with an identity element.
:::::::
::::::::
... Now you know monoid, let's see the definition of group.
(S, ⋅) is a group is it is a monoid such that every element has an
unique inverse.
:::::::::