Add to ORKGAbstract. It is popularly believed that Cantor's diagonal argument proves that there are more reals than integers. In fact, it proves only that there is no onto function from the integers to the reals; by itself it says nothing about the sizes of sets. Set size measurement and comparison, like all mathematics, should be chosen to fit the needs of an application domain. Cantor's countability relation is not a useful way to compare set sizes
When children play Superheroes and constantly try to one-up each other’s powers, it’s not unusual fo...
In 1891 Georg Cantor proved that there exist multiple size of infinity. In particular, the size of t...
Many of the ideas of mathematics have come about because of certain properties of the real numbers. ...
Abstract. It is popularly believed that Cantor's diagonal argument proves that there are more r...
Abstract. Recent work has defended “Euclidean ” theories of set size, in which Cantor’s Principle (t...
Recent work has defended “Euclidean” theories of set size, in which Cantor’s Principle (two sets hav...
The nave idea of \size " for collections seems to obey both to Aris-totle's Principle: \th...
The naıve idea of “size” for collections seems to obey both to Aristotle’s Principle: “the whole is ...
zAbstract Cantor's theory of cardinality violates common sense. It says. for example. that all ...
We discuss two main ways in comparing and evaluating the size of sets: the "Cantorian" way, grounded...
At the heart of mathematics is the quest to find patterns and order in some set of similar structures...
We introduce a "Euclidean" notion of size (numerosity) for "Punktmengen", i.e. sets of points of Euc...
In many areas ofmathematics problems of small divisors, or exceptional sets on which certain desired...
The Cantor set Ω is a rather remarkable subset of [0, 1]. It provides us with a wealth of interestin...
<p>A short (2-page) proof that the set of positive integers (i.e. {1, 2, 3, ...}) is finite in size,...
When children play Superheroes and constantly try to one-up each other’s powers, it’s not unusual fo...
In 1891 Georg Cantor proved that there exist multiple size of infinity. In particular, the size of t...
Many of the ideas of mathematics have come about because of certain properties of the real numbers. ...
Abstract. It is popularly believed that Cantor's diagonal argument proves that there are more r...
Abstract. Recent work has defended “Euclidean ” theories of set size, in which Cantor’s Principle (t...
Recent work has defended “Euclidean” theories of set size, in which Cantor’s Principle (two sets hav...
The nave idea of \size " for collections seems to obey both to Aris-totle's Principle: \th...
The naıve idea of “size” for collections seems to obey both to Aristotle’s Principle: “the whole is ...
zAbstract Cantor's theory of cardinality violates common sense. It says. for example. that all ...
We discuss two main ways in comparing and evaluating the size of sets: the "Cantorian" way, grounded...
At the heart of mathematics is the quest to find patterns and order in some set of similar structures...
We introduce a "Euclidean" notion of size (numerosity) for "Punktmengen", i.e. sets of points of Euc...
In many areas ofmathematics problems of small divisors, or exceptional sets on which certain desired...
The Cantor set Ω is a rather remarkable subset of [0, 1]. It provides us with a wealth of interestin...
<p>A short (2-page) proof that the set of positive integers (i.e. {1, 2, 3, ...}) is finite in size,...
When children play Superheroes and constantly try to one-up each other’s powers, it’s not unusual fo...
In 1891 Georg Cantor proved that there exist multiple size of infinity. In particular, the size of t...
Many of the ideas of mathematics have come about because of certain properties of the real numbers. ...