Galileo Galilei Quotes

And what is the greatest number? Number one.

There are infinite numbers between 0 and 1.

Some infinities are bigger than other infinities.

No one shall expel us from the paradise that Cantor has created for us.

Infinites, when considered absolutely without any restriction or limitation, are neither equal nor unequal, nor have any certain proportion one to another, and therefore, the principle that all infinites are equal is a precarious one.

I maintain that two and two would continue to make four, in spite of the whine of the amateur for three, or the cry of the critic for five.

I recall being fascinated by numbers even at age three and viewed their manipulation as a kind of game.

Set theory in sheep's clothing.

I’m so tired... I was up all night trying to round off infinity.

Number, the most excellent of all inventions.

A googolplex is precisely as far from infinity as is the number 1... no matter what number you have in mind, infinity is larger still.

The sum total of all sums total is eternal.

[On Cantor's work:] The finest product of mathematical genius and one of the supreme achievements of purely intellectual human activity.

Nature does not count nor do integers occur in nature. Man made them all, integers and all the rest, Kronecker to the contrary notwithstanding.

Mathematics may be defined as the economy of counting. There is no problem in the whole of mathematics which cannot be solved by direct counting.

Every transfinite consistent multiplicity, that is, every transfinite set, must have a definite aleph as its cardinal number.

To choose one sock from each of infinitely many pairs of socks requires the Axiom of Choice, but for shoes the Axiom is not needed.

Always is no Time at all.

I agree that two times two makes four is an excellent thing; but if we are dispensing praise, then two times two makes five is sometimes a most charming little thing as well.

We cannot ... prove geometrical truths by arithmetic.

Well, since paradoxes are at hand, let us see how it might be demonstrated that in a finite continuous extension it is not impossible for infinitely many voids to be found.

In a race, the quickest runner can never overtake the slowest, since the pursuer must first reach the point whence the pursued started, so that the slower must always hold a lead.

Can you do Division? Divide a loaf by a knife - what's the answer to that?

If we consider eternity, into that time never entered; eternity is not an everlasting flux of time, but time is as a short parenthesis in a long period; and eternity had been the same as it is, though time had never been.

The final end of Eternity, and the beginning of Infinity