In order for there to be a variable quantity in some mathematical study, the domain of its variability must strictly speaking be known beforehand through a definition. However, this domain cannot itself be something variable, since otherwise each fixed support for the study would collapse. Thus this domain is a definite, actually infinite set of values. Hence each potential infinite, if it is rigorously applicable mathematically, presupposes an actual infinite.
Georg CantorRelated topics
actual collapse definite definition domain infinite known order potential quantity set something speaking study support thus variability variableRelated quotes
In all cultures, it is the task of a religion to close the field of contingency ...and to set up havens of the absolute where it is possible to be led from acting to listening, from having to being, from planning to hoping, from judging to forgiving - from the finite into the infinite. A society in which such open spaces of eternity do not exist or are only insufficiently developed dies of itself due to lack of air to breathe.
Eugen Drewermann
I've seen a lot of patriots and they all died just like anybody else if it hurt bad enough and once they were dead their patriotism was only good for legends it was bad for their prose and made them write bad poetry. If you are going to be a great patriot i.e. loyal to any existing order of government (not one who wishes to destroy the existing for something better) you want to be killed early if your life and works won't stink.
Ernest Hemingway
When one admits that nothing is certain one must, I think, also admit that some things are much more nearly certain than others. It is much more nearly certain that we are assembled here tonight than it is that this or that political party is in the right. Certainly there are degrees of certainty, and one should be very careful to emphasize that fact, because otherwise one is landed in an utter skepticism, and complete skepticism would, of course, be totally barren and completely useless.
Bertrand Russell
When the sacred manifests itself in any hierophany, there is not only a break in the homogeneity of space; there is also a revelation of an absolute reality, opposed to the nonreality of the vast surrounding expanse. The manifestation of the sacred ontologically founds the world. In the homogenous and infinite expanse, in which no point of reference is possible and hence no orientation can be established, the hierophany reveals an absolute fixed point, a center.
Mircea Eliade
One might ask why the teachers do not notice the difficulty children have in learning BASIC. The answer is simple: Most teachers do not expect high performance from most students, especially in a domain of work that appears to be as "mathematical" and "formal" as programming. Thus the culture's general perception of mathematics as inaccessible bolsters the maintenance of BASIC, which in turn confirms these perceptions.
Seymour Papert
