Define “Infinite”

Unlock your mathematical superpowers

Fabio Turel
5 min readDec 12, 2021


Can you tell me what infinite is, and a sure way to tell whether something is infinite or not?

Easy, you might say. Like 1,2,3,… just go on forever.

But this would be just an example, not a definition. And, most of all, you can’t go on forever. I asked you to tell me what infinite is. Not what it would be, if only you could go on forever.

The Italian poet Giacomo Leopardi succeeds at evoking the feeling of awe that comes with our attempt to face infinity. He uses a suggestive comparison between the reality surrounding himself while in a state of contemplation, and the unknown space beyond a hedge.

Always to me beloved was this lonely hillside
And the hedgerow creeping over and always hiding
The distances, the horizon’s furthest reaches.

A hedge under a blue sky, blocking the view of the horizon.
Photo by qimono on Pixabay

But as I sit and gaze, there is an endless
Space still beyond, there is a more than mortal
Silence spread out to the last depth of peace,
Which in my thought I shape until my heart
Scarcely can hide a fear. And as the wind
Comes through the copses sighing to my ears,
The infinite silence and the passing voice
I must compare: remembering the seasons,
Quiet in dead eternity, and the present,
Living and sounding still. And into this
Immensity my thought sinks ever drowning,
And it is sweet to shipwreck in such a sea.

It is indeed one of the finest achievements of poetry, and a great way to exemplify Kant’s statement that the sublime is our own experience of being drawn to the infinite. But it is not a definition: it does not help us decide with absolute certainty if something is finite or not.

The definition



Fabio Turel

A Project Manager must be a good storyteller. Stories about my profession, my interests and my passions converge in this place.