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What is Newman's “infinite number of curves”?

In John Henry Newman's The Idea of a University (c. 1850), he writes that, in mathematical science, we are told of ...the existence of an infinite number of curves, which are able to divide a ...
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4answers
280 views

Is there a formal distinction between potential and actual infinities?

In modern set theory the difference between actual infinity and potential infinity is often not understood or even denied. Some decades back however mathematicians like Hilbert or Poincaré, let alone ...
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1answer
134 views

Why was Kronecker dissatisfied with Cantor's submitted paper?

It is said here that "In 1874 Cantor published an article in Crelle's Journal which marks the birth of set theory. A follow-up paper was submitted by Cantor to Crelle's Journal in 1878 but already set ...
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1answer
153 views

The ancient concept of Finite Space

How do you think it possible for the ancients to be satisfied with the concept of FINITE SPACE, with "fixed stars" at its limits? To our minds, the idea of infinite extension comes so naturally, ...
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1answer
311 views

What are the origins of Galileo's paradox?

Galileo's paradox is the observation that the natural numbers can be put into one to one correspondence with the square numbers, showing that an infinite set can be bijected to a proper subset of ...