[37] We say that a variable quantity becomes infinitely small when its numerical value decreases indefinitely in such a way as to converge towards the limit zero. It is worth remarking on this point that one ought not confuse a constant decrease with an indefinite decrease. The area of a regular polygon circumscribed about a given circle decreases constantly as the number of sides increases, but not indefinitely, because it has as its limit the area of the circle.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2009 Springer Science+Business Media, LLC
About this chapter
Cite this chapter
Bradley, R.E., Sandifer, C.E. (2009). On infinitely small and infinitely large quantities, and on the continuity of functions. Singular values of functions in various particular cases.. In: Cauchy’s Cours d’analyse. Sources and Studies in the History of Mathematics and Physical Sciences. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-0549-9_2
Download citation
DOI: https://doi.org/10.1007/978-1-4419-0549-9_2
Published:
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4419-0548-2
Online ISBN: 978-1-4419-0549-9
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)