# What’s the opposite of infinity? | Elevator Pitch

Do you remember the quote, "to infinity and beyond"? Well how can you go beyond infinity and what's the opposite of infinity? I'm about to jump in an elevator and find out I hear you're going to try and teach me some maths and I'm not the best with numbers so I think you might have your work cut out for you Everyone's great with numbers They just don't realize they're good with numbers yet Or no one's talked to them about numbers in a way that makes sense to

Them Don't disappoint me! Let's go Okay so what is infinity? Okay so infinity as you said is this concept that we use to describe something that doesn't have a bound Right so if we think of the natural numbers which are just the counting numbers like 1, 2, 3, 4, 5, etc It's something bigger than that Naturally So it's not actually a number but it's something that's a number can tend towards so nothing ever

Reaches infinity it just can get closer to infinity So how is infinity useful to us? So I mean for me, I work with lots of different systems that change with time So I like to look at what happens to something as time moves into the future Right So if I have like a pond of fish and I wanna know like what is – is there something that's gonna limit that population of fish? So maybe there's not

Food, not enough space So I want to look at what happens in the future Like do I pick five years in the future? Do I pick 10 years in the future? It's all kind of arbitrary If I look at what happens in that system as T tends to infinity Yeah Then I'm gonna see maybe some kind of limiting behavior like the fish is going to reach a population It's gonna blow up whatever So you use it to describe something Ok so it sets the point so far that it always allows you to find the limit? Yeah

Exactly Yeah What's the opposite of infinity? So in it depends! So, if I'm talking about infinity as a concept of being unbounded, the opposite would be something that's finite If I'm talking about time into the future, it will be time in the past It depends on what it is you're using infinity Right yeah sure And so you know be an infinite amount of time in the past but then if I put something like infinitely big, it would be something

Infinitesimally small So think – Woah! Let me just stop you there because we're halfway through and I have a lot of questions about infinitesimally small Yeah it's not a great word to say No it's not and it's not a great concept to think about if I'm being honest because how can something be infinitesimally small? Well okay so actually in reality like it's quite hard for it to be but mathematically it's very easy for it to be So if I I've got like a radioactive substance and I'm

Talking about its half-life so the amount of time it takes for the quantity of radioactive substance to halve Yep Right so after one half-life it will halve, after another one, it will halve and it will halve and it will halve and it will halve So it will never actually reached zero because I'm still halving something that's not zero It's just like so many decimal places Yeah yeah but in reality like eventually you're gonna get to that last like atom and it's gonna decay and there'll be

Nothing there Yeah So that's when mathematically something can be infinitesimally small in reality, you sort of do hit zero Would we ever go that far? Or is it just so that we don't have a limit on things and we can kind of find the limit? Yes so it's more it's the mathematical equations that give you this behavior as time goes to infinity but in reality like there's the smallest

Kind of subatomic particle we can't get smaller than that So infinity's kind of like a tool to let us find the limits It's a tool It's exactly, that's exactly it It's a really big tool Haha Or a really really tiny tool Or a tiny tool Awesome I think I nailed Yeah I reckon you did too Thank you No worries Yes!

When you think about it infinity's a term that gets used casually quite a lot and that starts to kind of dilute what it means to us and we don't think about it as deeply so it's really interesting to kind of deep dive into what infinity actually means and to realise that as humans we're used to applying our physical understanding of the world on to pretty much everything So when you do that and you say infinity is something that means that there is no bounds It

Kind of doesn't make sense We don't understand how that can be because there's always physical bounds But when you reframe it as a mathematical concept or a tool it makes a lot of sense It's something that we can use to find those physical limits that we're used to and I really like knowing that It's cool to be able to reframe and realise that I think of things in terms of human physicality when that doesn't always need to apply You know infinity is just kind of a way

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