# From Sets and Functions to the Tends-To Relation

Establish a foundational chain from set membership through total functions to convergence semantics.

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This is a suggested learning sequence, not a universal logical dependency or a formal proof.


- Stage 1 · required



## [Set membership](/en/mko/mko-set-membership/?from=%2Fen%2Fpaths%2Fpath-function-to-limits%2F%3Ffrom%3D%252Fen%252Fpaths%252F)

Establish the basic relation between an element and a set.

[Related questions](/en/explore/?mko=mko-set-membership) [Concept guides](/en/derivations/?q=mko-set-membership)


- Stage 2 · required



## [Function mapping](/en/mko/mko-function-mapping/?from=%2Fen%2Fpaths%2Fpath-function-to-limits%2F%3Ffrom%3D%252Fen%252Fpaths%252F)

Understand a total function from a domain to a codomain.

[Related questions](/en/explore/?mko=mko-function-mapping) [Concept guides](/en/derivations/?q=mko-function-mapping)


- Stage 3 · required



## [Tends-to relation](/en/mko/mko-tends-to-relation/?from=%2Fen%2Fpaths%2Fpath-function-to-limits%2F%3Ffrom%3D%252Fen%252Fpaths%252F)

Introduce approach and the filter core on top of function relations.

[Related questions](/en/explore/?mko=mko-tends-to-relation) [Concept guides](/en/derivations/?q=mko-tends-to-relation)



Path source & statuspath-function-to-limits · reviewed

[Original paths JSON](/data/architecture/learning-paths.json)