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Infinite limits

Level FundamentalDifficulty ★★★★★Concept⌖ Open in the map

What is it?

$f(x) \to \pm\infty$ as $x \to a$ : the function grows without bound near a point, as $1/x$ near 0. The graph has a vertical asymptote there.

Formulas

\lim_{x\to a} f(x) = +\infty \iff \forall M\ \exists\delta > 0:\ 0 < |x - a| < \delta \Rightarrow f(x) > M

Where it shows up in computing

Floating point (IEEE 754)★★★★★frequentScientific computing and algorithms
IEEE 754 has $\pm\infty$ : 1.0/0.0 is inf, a finite stand-in for an infinite limit.

Where is it used?

Computing topics reachable from here, through the chain of ideas that leads to them:

λ Scientific computing and algorithms

Floating point (IEEE 754)★★★★★
Floating point (IEEE 754)→Scientific computing★★★★★

This page has the essentials. A fuller treatment (intuition, formal definition, worked example) is on the way.