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# Questions tagged [infinity]

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8 votes
1 answer
324 views

### Did Gauss criticize cardinals?

In a well-known passage, Gauss criticized the use of infinity in mathematics in the following terms: I protest first of all against the use of an infinite quantity as a completed one, which is never ...
• 6,528
1 vote
0 answers
76 views

### Criticisms of the Dedekind's definition of infinite sets for violating Euclid's Common Notion 5

Dedekind's definition of the infinite set says in its essence that part may be equal to the whole contradicting Euclid's Common Notion 5 stating that "the whole is greater than the part." ...
• 349
3 votes
0 answers
81 views

### Earliest historical work on Cauchy's infinitesimal delta functions?

As early as 1981, Hans Freudenthal briefly mentioned Cauchy's work on "singular integrals (i.e., integrals of infinitely large functions over infinitely small paths [$\delta$ functions])" on ...
• 6,528
3 votes
2 answers
277 views

### History of Infinity: How does the idea of infinite set become widely accepted?

It seems pretty strange to me that the idea of infinity and infinite sets was initially opposed by many prominent Mathematicians, even driving Cantor into depression. However, in modern days, everyone ...
• 159
3 votes
2 answers
301 views

### In which article/book chapter did Cantor, Hilbert, and Poincaré formally define or directly discusse the term “potential infinity”?

Some media sources say that "Cantor claimed that there would only be potential infinity, not actual infinity" In addition, the following link claims that Hilbert, Poincaré, and Cantor were ...
• 133
5 votes
1 answer
483 views

### 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 ...
• 487
7 votes
4 answers
728 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 ...
2 votes
1 answer
163 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, ...
• 217
9 votes
1 answer
1k 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 ...
• 1,355
6 votes
2 answers
392 views

### Did Leibniz use infinite numbers?

Arthur's recent article Arthur, Richard T. W. Leibniz's actual infinite in relation to his analysis of matter. G. W. Leibniz, interrelations between mathematics and philosophy, 137–156, Archimedes, ...
• 6,528
27 votes
2 answers
1k views

### Did Galileo's writings on infinity influence Cantor?

To what extent was Cantor motivated by Galileo's paradox? More generally, to what extent were late 19th century mathematicians motivated by, or even aware of, Galileo's paradox? This is an issue I've ...
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