What I assert and believe to have demonstrated in this and earlier works is that following the finite there is a transfinite (which one could also call the supra-finite), that is an unbounded ascending lader of definite modes, which by…

Quote by Georg Cantor

Topics: Infinity Quotes, Mathematics Quotes

A set is a Many that allows itself to be thought of as a One.

A set is a Many that allows itself to be thought of as a One.

The transfinite numbers are in a certain sense themselves new irrationalities and in fact in...

The transfinite numbers are in a certain sense themselves new irrationalities and in fact in...

The fear of infinity is a form of myopia that destroys the possibility of seeing...

The fear of infinity is a form of myopia that destroys the possibility of seeing...

The essence of mathematics lies in its freedom.

The essence of mathematics lies in its freedom.

In mathematics the art of proposing a question must be held of higher value than...

In mathematics the art of proposing a question must be held of higher value than...

I realise that in this undertaking I place myself in a certain opposition to views...

I realise that in this undertaking I place myself in a certain opposition to views...

The actual infinite arises in three contexts: first when it is realized in the most...

The actual infinite arises in three contexts: first when it is realized in the most...

A billion stars go spinning through the night, blazing high above your head. But in...

A billion stars go spinning through the night, blazing high above your head. But in...

If a thing loves, it is infinite.

If a thing loves, it is infinite.

I must study politics and war that my sons may have liberty to study mathematics...

I must study politics and war that my sons may have liberty to study mathematics...

I was good at math before they decided to mix the alphabet in it.

I was good at math before they decided to mix the alphabet in it.

Mathematicians, who are only mathematicians, have exact minds, provided all things are explained to them...

Mathematicians, who are only mathematicians, have exact minds, provided all things are explained to them...

But there is another reason for the high repute of mathematics: it is mathematics that...

But there is another reason for the high repute of mathematics: it is mathematics that...

We do not learn by inference and deduction and the application of mathematics to philosophy,...

We do not learn by inference and deduction and the application of mathematics to philosophy,...

Yes, we have to divide up our time like that, between our politics and our...

Yes, we have to divide up our time like that, between our politics and our...

Philosophy is written in that great book which ever lies before our eyes ... We...

Philosophy is written in that great book which ever lies before our eyes ... We...

Some mathematician has said pleasure lies not in discovering truth, but in seeking it.

Some mathematician has said pleasure lies not in discovering truth, but in seeking it.

A formal manipulator in mathematics often experiences the discomforting feeling that his pencil surpasses him...

A formal manipulator in mathematics often experiences the discomforting feeling that his pencil surpasses him...

The piano's world encompasses glass-nerved virtuosi and stomping barrel-housers in fedoras; it is a world...

The piano's world encompasses glass-nerved virtuosi and stomping barrel-housers in fedoras; it is a world...

I heard you're good in algebra, can you replace my 'X' without asking 'Y?'

I heard you're good in algebra, can you replace my 'X' without asking 'Y?'