TeXipedia

real

Denotes the set of real numbers in mathematical notation, representing all points on a continuous number line.

Overview

Essential in mathematical expressions across numerous fields, particularly in analysis, algebra, and applied mathematics.

  • Fundamental in defining number systems and mathematical domains
  • Used extensively in function definitions and domain specifications
  • Common in constraints and conditions for mathematical proofs
  • Appears frequently in optimization problems and mathematical modeling
  • Critical for expressing continuous variables and numerical ranges

Examples

Expressing the real part of a complex number z.

ℜ(z)=ℜz=x\Re(z) = \real z = x 
\Re(z) = \real z = x

Showing the real part in Euler's formula.

ℜ(eix)=cos⁡x\real(e^{ix}) = \cos x 
\real(e^{ix}) = \cos x

Real part of a complex exponential function.

ℜ(1+i)n=ℜ(2neinπ/4)\real(1 + i)^n = \real\left(\sqrt{2}^n e^{in\pi/4}\right) 
\real(1 + i)^n = \real\left(\sqrt{2}^n e^{in\pi/4}\right)