Function

0.1 Introduction

Instance of:

0.2 Frequentist

AKA: \(f: X \mapsto Y\), \(f(x)\), map, mapping, linear map, linear function, transformation, morphism

Distinct from:

English: A function from a set X to a set Y is an assignment of an element of Y to each element of X. The set X is the domain, and the set Y is the codomain.

Formalization:

The formalization is annoying in that there are multiple conventions for writing a function which are equivalent.

Psuedo code

f = function(X){
  Y=X+1 #some operation
  return(Y)
}

Where the domain is all flatoing point numbers and so is the codomain (up to the precision of the computer).

That can also be written.

\[ f: X \mapsto Y \] Where \(f\) is the name of the function, \(\mapsto\) is the “maps to” or “Maplet” symbol.

Cites: Wikipedia ; Wikidata ; Wolfram

Code

Examples:

library(DBI)
# Create an ephemeral in-memory RSQLite database
#con <- dbConnect(RSQLite::SQLite(), dbname = ":memory:")
#dbListTables(con)
#dbWriteTable(con, "mtcars", mtcars)
#dbListTables(con)

#Configuration failed because libpq was not found. Try installing:
#* deb: libpq-dev libssl-dev (Debian, Ubuntu, etc)
#install.packages('RPostgres')
#remotes::install_github("r-dbi/RPostgres")
#Took forever because my file permissions were broken
#pg_lsclusters
require(RPostgres)

Loading required package: RPostgres

# Connect to the default postgres database
#I had to follow these instructions and create both a username and database that matched my ubuntu name
#https://www.digitalocean.com/community/tutorials/how-to-install-postgresql-on-ubuntu-20-04-quickstart
con <- dbConnect(RPostgres::Postgres())

import torch

0.3 Bayesian

English: Formalization:

\[ \]

Cites:

Code