Mathematical/logic proof that unicorns exist.

@Luke73 Thank you. Yes, I understand that, but I have never seen any mention of sets or need for them in any technical mathematics, even at levels far above anything I could have attained, hence my concern that about needless use.

Even when used as in your example of a square joining a set of 4 points, the use was purely colloquial, just linguistic convenience. Similarly with graphs: no formal use of "set" beyond a basic comment that it's a set of co-ordinates. Not diving into Set Theory where it's not necessary.

@ArishMell It’s taught and used in any course at higher mathematics at university. I know people from different fields and people who teach it too. For example in calculus, you can’t do it without it. For example for the intermediate value theorem or for splitting and combining integrals.

And no, typically a square contains more than four points. In the real plane a square contains infinite many points. So for example when you check if two figures intersect, you check if the union of these two sets is non-empty basically.

Another example where it’s necessary to understand sets is when making multiple graphs in one figure. Usually you want the graphs to share an axis, so you want the domains to be the same, or at least a subset of the biggest one.

@Luke73 Thankyou for the explanation but the more you show its subleties, the more Set Theory seems a mathematical analysis of maths for its own sake.

I am used to using simple maths, and came into contact with far more advanced mathematics - including calculus to a high level - and none of it uses sets. I can see you can describe a graph or a geometricall figure or perhaps an equation in terms of sets, and can see it being relevant to statistics almost by definition, but it is not necessary to learn Set Theory to learn most mathematics. Let alone to use mathematics for anything practical, whether as simple as the area of a circle or in very advanced engineering designs.

Instead all the maths I was taught - and all the books I have - go straight to the point. They don't battle through thickets of sets for everything, not even calculus taught from First Principles.

I had no idea Sets are even involved in the diagonal of a square or a complex harmonic analysis! You just dive straight in with the appropriate equations - though I know harmonic analysis does involve fiendish trigonometrical and logarithmic series.

+++++

This reminds me slightly of when I used to contribute to a site called "Answers.com", part of Wikipedia. (It closed then later re-opened but by subscription, which I refuse on principle though I sometimes donate to Wiki. itself.)

Answers is or was a classified Q&A knowledge site on a huge range of topics. The Mathematics included many Americans trying to learn US / ISO measurements conversions. Already used to metric measures, I helped two groups of questioners.

One was householders calculating the doses for their private swimming-pools measured in feet, of disinfectant sold in metric units with metric instructions. I walked them through the arithmetic, step by step. Some did not realise you need the volume of water, not its surface area.

The other appeared to be school-children trying to learn the basics: feet to metres, miles to km, gallons to litres. I would not help them cheat by just giving the answers as some respondents did. Instead I also told them how: look up the appropriate, widely published conversion constant, and multiply accordingly. Just simple A = B X conversion, "times sums".*

The homework questions were spoilt by two characters making its as baffling as possible; probably deliberately. They did not use over-analysis as your beloved Sets do, but strange over-conversions[/]. They used the word "Algebra" but no algebra itself, and referred to a text-book on "Dimensional Analysis", which this is [i]not. They often made mistakes in their own sums, too! E.g., Miles to km? So miles to inches to centimetres (non-"Preferred" units anyway), back up to km.

.........

*(I ensured I used US, not UK, Gallons. For miles to km I suggested 8/5 is usually simple enough for mental arithmetic, and sufficiently accurate for most real journeys.)

@Inanna My condolence? haha

@Inanna Been a victim of intellectual assault!

@busty78 What part of it? In what way?

@Luke73mythical