fundamental sequence

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noun Mathematics.

an infinite sequence, x1, x2, …, whose terms are points in Ek, in which there exists a point y such that the limit as n goes to infinity of xn = y if and only if for every ε>0, there exists a number N such that i>N and j>N implies |xi −xj|< ε.

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Also called Cauchy sequence, convergent sequence .

Compare complete (def. 10b).

Origin of fundamental sequence

First recorded in 1865–70

Words nearby fundamental sequence

fundamentalism, fundamentalist, fundamental law, fundamentally, fundamental particle, fundamental sequence, fundamental star, fundamental unit, funded debt, fundholding, fundi

How to use fundamental sequence in a sentence

These fundamental sequences, captured in its genome, allow its survival.
A Language AI Is Accurately Predicting Covid-19 ‘Escape’ Mutations|Shelly Fan|January 19, 2021|Singularity Hub
Everyone out there who says, “Charlie Hebdo provoked,” is making the same fundamental error.
Ayaan Hirsi Ali: Our Duty Is to Keep Charlie Hebdo Alive|Ayaan Hirsi Ali|January 8, 2015|DAILY BEAST
And with the dance sequence, we wanted something very physical.
Coffee Talk with Fred Armisen: On ‘Portlandia,’ Meeting Obama, and Taylor Swift’s Greatness|Marlow Stern|January 7, 2015|DAILY BEAST
So too with a vaccine that provokes a specific immune response aimed at a specific RNA sequence.
When You Get the Flu This Winter, You Can Blame Anti-Vaxxers|Kent Sepkowitz|January 1, 2015|DAILY BEAST

This is a testament to the fundamental human—and American—desire to combine place and possibility.
Will Texas Stay Texan?|David Fontana|December 29, 2014|DAILY BEAST
In the meantime, we continue to support the restoration of fundamental human rights in Cuba.
Why Congress Hates Your Cuban Rum|Tim Mak|December 19, 2014|DAILY BEAST
Besides this fundamental or primary vibration, the movement divides itself into segments, or sections, of the entire length.
Expressive Voice Culture|Jessie Eldridge Southwick
What the ear hears is the fundamental pitch only; the overtones harmonize with the primary or fundamental tone, and enrich it.
Expressive Voice Culture|Jessie Eldridge Southwick
Not only have its fundamental principles been fully vindicated but in most details the working of the measure has been successful.
Readings in Money and Banking|Chester Arthur Phillips
Judge for yourself the difficulty surrounding the remainder of the symbols and fundamental truths of christianity.
The Jesuit Relations and Allied Documents, Vol. II: Acadia, 1612-1614|Various
And hence the reader can notice the fundamental difference between all other methods and mine.
Assimilative Memory|Marcus Dwight Larrowe (AKA Prof. A. Loisette)