=1948.= Infinity is the land of mathematical hocus pocus. There Zero the magician is king. When Zero divides any number he changes it without regard to its magnitude into the infinitely small [great?], and inversely, when divided by any number he begets the infinitely great [small?]. In this domain the circumference of the circle becomes a straight line, and then the circle can be squared. Here all ranks are abolished, for Zero reduces everything to the same level one way or another. Happy is the kingdom where Zero rules!--CARUS, PAUL. _Logical and Mathematical Thought; Monist, Vol. 20 (1909-1910), p. 69._ =1949.= Great fleas have little fleas upon their backs to bite ’em, And little fleas have lesser fleas, and so _ad infinitum._ And the great fleas themselves, in turn, have greater fleas to go on; While these again have greater still, and greater still, and so on. --DE MORGAN, A. _Budget of Paradoxes (London, 1872), p. 377._ =1950.= We have adroitly defined the infinite in arithmetic by a loveknot, in this manner ∞; but we possess not therefore the clearer notion of it.--VOLTAIRE. _A Philosophical Dictionary; Article “Infinity.” (Boston, 1881)._ =1951.= I protest against the use of infinite magnitude as something completed, which in mathematics is never permissible. Infinity is merely a _facon de parler_, the real meaning being a limit which certain ratios approach indefinitely near, while others are permitted to increase without restriction.--GAUSS. _Brief an Schumacher (1831); Werke, Bd. 8 p. 216._ =1952.= In spite of the essential difference between the conceptions of the _potential_ and the _actual_ infinite, the former signifying a _variable_ finite magnitude increasing beyond all finite limits, while the latter is a _fixed_, _constant_ quantity lying beyond all finite magnitudes, it happens only too often that the one is mistaken for the other.... Owing to a justifiable aversion to such _illegitimate_ actual infinities and the influence of the modern epicuric-materialistic tendency, a certain _horror infiniti_ has grown up in extended scientific circles, which finds its classic expression and support in the letter of Gauss [see 1951], yet it seems to me that the consequent uncritical rejection of the legitimate actual infinite is no lesser violation of the nature of things, which must be taken as they are.--CANTOR, G. _Zum Problem des actualen Unendlichen; Natur und Offenbarung, Bd. 32 (1886), p. 226._