How is it that humans cannot grasp the concept of infinity?

Infinity is a notion that can make you dizzy and is related to various dimensions as space, time, mass and temperature. In the large (for example the ever expanding universe), in the small (the smallest particles that were discovered recently are not the smallest) and in the middle. I remember an episode of van Kooten and de Bie, where de Bie explains that to get from A to B you first have to cover half that distance. And of every half again a half. And so you need to cover an infinity of halves-of-distances. And yet it is possible to move from A to B… In short it fascinates me why infinity is so hard to grasp. And emotionally it has everything to do with the how and why of our existence

This question looks like an earlier one but it makes a very strong assumption: the question poser supposes that nobody can grasp the notion of `infinity’. That seems to me to be a strong statement, there must be people that at least think they grasp infinity and why should we doubt them? The example is another variant of one of Zeno’s paradoxes and we saw those before with reference to the same satirists as above.

The mathematician has in any case learned to form an image of the infinite in its two manifestations: something that is larger than all real numbers, denoted ∞, and as `the number of elements’ of sets like that of the natural numbers, rational numbers, real numbers etcetera. In both cases those notions have unambiguous definitions that are very good to work with. The next few days I’ll talk about those definitions some more.

Also: `infinite’ is the antonym of `finite’; if we want to know what infinite means we must also know what finite means. Something to ponder: what does `finite’ actually mean?

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Read all of KP Hart’s math questions here! If you have any questions for KP Hart, tweet us or leave them in the comment section below!

About Dutch Mathematician KP Hart: In the beginning of this year the Dutch government opened a website, The Dutch Science Agenda, where everyone could post questions that they thought were of scientific interest. This was an attempt to involve the whole country in determining what the Dutch science agenda should be in the coming years.

I looked through the questions and searched for terms like `mathematics’, `infinity’ … to see what mathematical questions there were and I noticed various questions that already have answers (and have had for a long time). On a whim I decided to post answers to those questions, in Dutch. For your edification I will translate these posts into English.