1.2.5

Notation in Mathematical Arguments

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Notation in Mathematical Arguments

When studying maths at a higher level, you need to be able to write mathematical arguments using the correct notation.

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Implies

  • The implies symbol is a type of arrow written as \Rightarrow.
  • We use this symbol to show when one equation implies that another equation is true.
  • For example, x=5x = 5 implies that x2=25x^2 = 25.
  • So we can write x=5x2=25x = 5 \Rightarrow x^2=25
  • Note that this relationship only goes one way, as x2=25x^2=25 does not imply that x=5x=5 as it could also equal −5.
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Equivalence

  • The double-ended arrow symbol \Leftrightarrow is used to show when two equations are equivalent.
  • This means that one equation being true implies the other is true, and vice versa.
  • For example, x2y2=9(x+y)(xy)=9x^2 - y^2 = 9 \Leftrightarrow (x+y)(x-y) = 9
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Therefore

  • The symbol for the word 'therefore' is , which is a triangle of three dots.
  • The symbol does not show a relation between equations, but is used as shorthand instead of writing out the word 'therefore'.
  • For example, x=2ax = 2a, therefore xx is even.
    • So we can write x=2ax = 2a xx is even.
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Because

  • The symbol for the word 'because' is , which is an upside-down triangle of three dots.
  • The symbol does not show a relation between equations, but is used as shorthand instead of writing out the word 'because'.
  • For example, x2+1=5x^2 + 1 = 5 because x=2x = 2.
    • So we can write x=2,  x2+1=5x=2,\; x^2 +1=5

Jump to other topics

1Proof

2Algebra & Functions

2.1Powers & Roots

2.2Quadratic Equations

2.3Inequalities

2.4Polynomials

2.5Graphs

2.6Functions

2.7Transformation of Graphs

2.8Partial Fractions (A2 Only)

3Coordinate Geometry

4Sequences & Series

5Trigonometry

6Exponentials & Logarithms

7Differentiation

8Integration

9Numerical Methods

10Vectors

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