Cauchy defined infinitesimal as a variable or a function tending to zero, or as a null sequence.
While I found the definition is not so popular and nearly discarded in math according to the following statement.
(1). Infinitesimal entry in Wikipedia:
Some older textbooks use the term "infinitesimal" to refer to a
variable or a function tending to zero
Why textbooks involved with the definition is said to be old ?
(2). Robert Goldblatt, Lectures on the Hyperreals: An Introduction to Nonstandard Analysis, P15
(His = Cauchy's)
Why says 'Even'?
(3). Abraham Robinson, Non-standard analysis, P276
why Cauchy's definition of infinitesimal, along with his 'basic approach' was superseded?
Besides, I found most of the Real analysis or Calculus textbooks, such as Principles of mathematical analysis(Rudin) and Introduction to Calculus and Analysis(Richard Courant , Fritz John), don't introduce Cauchy's definition of infinitesimal, Why ?
Why Cauchy's definition of infinitesimal was unpopular and not widely used, and nearly discarded?
P.S. I refered some papers still cannot find the answer.
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