Every well-ordered set is isomorphic to an ordinal. Common notion, for example see Introduction to https://arxiv.org/abs/2409.07352

⊢((𝐴∈V∧𝑅We𝐴)↔∃𝑓(dom𝑓∈On∧𝑓IsomE,𝑅(dom𝑓,𝐴)))

\[ \vdash ( ( A \in \mathrm{V} \wedge R \mathrm{We} A ) \leftrightarrow \exists f ( \mathrm{dom} f \in \mathrm{On} \wedge f \mathrm{Isom} \mathrm{E} , R ( \mathrm{dom} f , A ) ) ) \]

Every well-ordered set is isomorphic to
a unique ordinal.

⊢((𝐴∈V∧𝑅We𝐴)↔∃!𝑜∈On∃𝑓∈(𝐴↑ₘ𝑜)𝑓IsomE,𝑅(𝑜,𝐴))

\[ \vdash ( ( A \in \mathrm{V} \wedge R \mathrm{We} A ) \leftrightarrow \exists{!} o \in \mathrm{On} \exists f \in ( A \uparrow_\mathrm{m} o ) f \mathrm{Isom} \mathrm{E} , R ( o , A ) ) \]

We can phrase the Axiom of Choice as "Every set injects into an ordinal."

⊢(CHOICE↔∀𝑥∃𝑜∈On𝑥≼𝑜)

\[ \vdash ( \mathrm{CHOICE} \leftrightarrow \forall x \exists o \in \mathrm{On} x \preccurlyeq o ) \]

#math #metamath #SetTheory #WellOrdering #OrdinalNumbers

If not , then we can define time this way and it's not even circular logic?
What is 0 units of time ?
Assumption: before relation exists and has meaning ( did i jump the gun?)
Amount of time taken by an event E to take place before E, followed by ski combinators or idk good ol induction ( , ll that imply #wellordering ?), You 1,2,3 .. units of time up to infinite time.
No language can be meaningful for all the words which belong to it
#Incompleteness

https://mathstodon.xyz/@xameer/109376766835598176