Machine Epsilon

Numerical Analysis · Axiom Academy

Understanding the fundamental unit of floating-point precision Imagine a number line where not every point exists—only certain "slots" are available. Machine epsilon measures how far apart adjacent slots are near 1.0. We can compute ε experimentally by repeatedly halving a value until adding it to 1 makes no difference: Machine epsilon tells us about relative precision . The absolute gap between representable numbers varies with magnitude. Machine epsilon sets the limit on numerical precision. Any computation introduces relative errors of at least ε/2.

This is the written version of the interactive lesson above. See the full Numerical Analysis course.