Is unique impossible?

[Jayhawker Soule]

Ecclesiastes 1:9

Only that shall happen
Which has happened,
Only that occur
Which has occurred;
There is nothing new
Beneath the sun!​

Given sufficient time, is the unique impossible?

 

[Evangelicalhumanist]

In an infinte amount of time, an infinite variety of anything at all is at least possible. And each could very well be unique.

Closer to home -- there will never be anyone precisely like me, or you, or @Jayhawker Soule. And try as often as you want, your Cacio e Pepe will not turn out precisely the same as any of your previous tries. (It might still be good, though. All of mine are.)

 

[Jayhawker Soule]

In an infinte amount of time, an infinite variety of anything at all is at least possible.

Who made up that rule? Based on what?

 

[Evangelicalhumanist]

Who made up that rule? Based on what?

Try this: start at the beginning of time (let's call it t0) and repeat to infinity (let's call it t∞), and at each step, simply add 1 to whatever number you chose to start with. Trust me, they will all be different.

Let me phrase it another way: do you know of a number that you could not add "1" to?