The Actual Infinite Arises In Three Contexts:

The Potential Infinite Means Nothing Other Than An Undetermined, Variable Quantity, Always Remaining Finite, Which Has To Assume Values That Either Become Smaller Than Any Finite Limit No Matter How Small, Or Greater Than Any Finite Limit No Matter How Great.

In Mathematics The Art Of Proposing A Question Must Be Held Of Higher Value Than Solving It.

I Am So In Favor Of The Actual Infinite That Instead Of Admitting That Nature Abhors It, As Is Commonly Said, I Hold That Nature Makes Frequent Use Of It Everywhere, In Order To Show More Effectively The Perfections Of Its Author. Thus I Believe That There Is No Part Of Matter Which Is Not - I Do Not Say Divisible - But Actually Divisible; And Consequently The Least Particle Ought To Be Considered As A World Full Of An Infinity Of Different Creatures.

Great Innovation Only Happens When People Aren't Afraid To Do Things Differently.

There Is No Doubt That We Cannot Do Without Variable Quantities In The Sense Of The Potential Infinite. But From This Very Fact The Necessity Of The Actual Infinite Can Be Demonstrated.