Avinoam Mann wrote few days ago:
> My second point is that Borzacchini jumps straight from Aristotelean
> science to Renaissance one, ignoring the Arab (or Muslim) science. It
> seems to me that the Arabs (of whatever nationality, recall previous
> discussions) are the real (no pun intended) inventors of real numbers.
> Possibly influenced by the Indians; for all that I'm going to India by
> the end of the day, I know very little about ancient Indian mathematics.
This was addressed subsequently by Luigi Borzacchini
Two further points
1
There is a reason for not jumping quite so far: Cantor considered
himself indebted to St Augustine (c. 400CE) who wrote, in City of God,
chapter 19, addressing the infinitude of God's knowledge:
..."though taken separately, each number is finite, yet, because they are
all unequal and different, taken together, they are infinite...
"Although then, there is no definite number corresponding to an infinite
number, an infinity of numbers is, nevertheless, not incomprehensible to
him..."
translation from Image Books edition (1958).
So actual infinites were considered by some pre Renaissance thinkers
2
Nonetheless the Simon first clear formulation of the concept of a
real number I'm aware of comes from Stevin (l'Arithmetique,1585, in Works
IIB 501):
"To a continuous magnitude corresponds the continuous number to which it is
attributed...Number is something in magnitude like wetness in water: it
penetrates like the latter into every part of the water; and just as to a
continuous water corresponds continuous wetness, so to a continuous number
corresponds a continuous magnitude."
also cf his Mathematical Theses in Works IIB p 738
Bob Berghout
Bob Berghout, rfb@frey.newcastle.edu.au
Department of Mathematics, University of Newcastle 2308
Ph: (+61 2) 4921 5546 FAX: (+61 2) 4921 6898