Definition:Substitution

Definition

Substitution is a word that denotes the process of replacement of every occurrence of a term in an expression or equation with another.

Disambiguation

This page lists articles associated with the same title. If an internal link led you here, you may wish to change the link to point directly to the intended article.

Substitution may refer to:

• Set Theory:
  • Definition:Substitution (Set Theory)

• Formal Systems:
  • Definition:Substitution (Formal Systems)
    • Definition:Substitution for Well-Formed Part
    • Definition:Substitution for Letter
      • Definition:Alphabetic Substitution
    • Definition:Substitution of Term
    • Definition:Substitution for Metasymbol

• Mathematical Logic:
  • Definition:Substitution (Mathematical Logic)

Examples

Arbitrary Example

Consider the expression:

$x^2 + 2 x + 6$

Substituting $2$ for $x$, we get:

$2^2 + 2 \times 2 + 6$

which evaluates to $14$.

This is called making the substitution $x = 2$.

If instead we making the substitution $x = y - 1$, the expression becomes:

$\paren {y - 1}^2 + 2 \paren {y - 1} + 6$

which simplifies to:

$y^2 + 5$

It is now easily seen that the expression cannot be less than $5$ in value, which happens when $y = 0$.

That is, when $x = -1$.

Also see

• Definition:Replacement

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): substitution
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): substitution

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• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): substitution