# Is money discrete or continuous?

Discussion in 'Mathematics' started by deleted456, Sep 10, 2007.

1. ### JSimpson

Always good to have an intellectual discussion!
OK, first, the Bank of England does not set the rules on trade. (Post on the Business Studies forum for more detail). They have 3 responsibilities: Setting the interest rate, issuing banknotes and maintaining a stable financial system. Note therefore that the smallest cash denomination they are responsible for is £5

Legal tender is a misunderstood term, but the Royal Mint have a good paragraph:

"Legal tender has a very narrow and technical meaning in the settlement of debts. It means that a debtor cannot successfully be sued for non-payment if he pays into court in legal tender. It does not mean that any ordinary transaction has to take place in legal tender or only within the amount denominated by the legislation. Both parties are free to agree to accept any form of payment whether legal tender or otherwise according to their wishes."

In other words, the value of a transaction is not restricted to the coins and notes in circulation.

The argument about whether continuous data has to be Real or rational is also false. Continuous data is defined as values that can be subdivided as far as you like, (and in reality will be limited by the measurement device.) Height or length are typical examples of continuous data, and no one is ever going to declare that they are pi metres tall.

I would go further and suggest that as the definition relies on subdivision of a unit quantity, continuous data will ALWAYS be rational.

All sources I can find that categorise money have it as continuous, with a few pointing out in addition that cash is discrete.

In the real world, transactions using fractions of a pence go on all the time. They may be limited to non cash scenarios, so you may not come across them but I can assure you they are there.

2. ### erm

I agree that this is a very useful debate. Particularly for the pupils themselves to have. What an excellent extension exercise for them, and what a wonderful tool for the teacher to assess exactly how far they understand the discrete/continuous concepts, their relevance, and how the work they are doing in the classroom relates to the real world.

I have always asked my brightest students this very question, and ask them to explain their reasoning. (I first ask them about UK shoe size, and follow with the money one for those who find the shoe size one too obvious.)

3. ### MrJob

I accept the point about the Royal Mint being responsible for coins, but it is still true to say that for all practical purposes money is discrete.

The original question was "Is money discrete or continuous?"

Examples.

1. A man wins £10 from the national lottery. How can he split the entire £10 so that each of his three children RECEIVE EXACTLY 1/3 rd of his winnings ?

3. Apples at my local supermarket are priced at 84.44p/kg. How can I pay 84.44 p for my kg of apples ?

Money is discrete to keep things simple.

4. ### salingers

I take issues with Mr Simpson's pythagorean claim that, "I would go further and suggest that as the definition relies on subdivision of a unit quantity, continuous data will ALWAYS be rational."

Let X be the set of lengths of hypotenuses of right-angled triangles with non-hypotenuse sides of rational length. This set certainly contains irrational values.

5. ### JSimpson

Not sure I understand about the triangles, but then I've just had lunch so my brain has slowed down.

My thought was that the definition of continuous data was that it was that the quantity being measured could be subdivided as much as you like.
In other words, all values must be of the form 1/N representing 1 unit (feet, metres, pounds) subdivided into N divisions, where N takes any integer value. As such, the result must be rational.

I am sure someone will argue that the divisions do not need to be equal, but I'm not sure that agrees with customary definitions or mechanisms of measurement.

6. ### penchoNew commenter

Mr Job.
Money is not discrete though. Every source I can find says it is continuous.

If you say to a pupil that it takes definite values such as 50p, 51p etc... Then you are saying other values are not possible. Which is not true. There are several everyday examples petrol (85.9p per litre) and BT phone call costs (5.5p minimum per call) - exchange rates (\$1 = £0.49253)

You simply cannot claim that money is discrete. Maybe you could say that the system of currency that we have allows us to pay in only discrete values. Not too sure.

But please do not say that money is discrete.

7. ### salingers

Pencho said, "But please do not say that money is discrete."

Will you now explain why it matters! Why is this debate important. What statistical treatment of financial data changes if money is continuous and not discrete?

If you can't answer this, I revert to my original claim: we're arguing about angels and pinheads.

8. ### penchoNew commenter

What do you mean why does it matter?

It matters because the statement MrJob makes is wrong. If Mr Job is willing to accept that then the discussion is over. He can't keep saying money is discrete because it is not.

The original question was "Is Money discrete or continuous?" I gave an answer of its continuous. You then came on and said does it actually matter? Well the answer is yes it does matter.

The OP wanted to know the answer and I gave a correct answer. You then tried to disagree along with Salingers. As a result it just seems you are now trying to say "what a pointless question in the first place". I was only trying to help out. If this subject is not important to you, why bother posting.

9. ### Polecat

If I remember correctly, the OP's question was in the context of Statistics. That is a branch of Applied Mathematics, which means we are talking about modelling. Whether we regard 'money' as discrete or continuous depends on the model. It can be either. Previous posters have provided plenty of examples.
It is an important question, and a very good one to raise with students.

10. ### salingers

I'm not being argumentative. I'm asking the legitimate question -- given that statistics is an applied science -- why does it matter whether money is discrete or continuous? If you can't give an example in which the status -- discrete or continuous -- of money determines two different analyses or results in two different conclusions, then the debate is of little practical value. In that case, I'm not sure that this is a good subject to discuss with students because it loses the focus of what statistics is about, i.e. modelling real-world phenomena in order better to understand them, to draw inferences and to make predictions. By obsessing on detail such as discrete/continuous students lose sight of the bigger -- and more important -- picture.

11. ### charmlessman

Nobody is wrong here- you are just using different interpretations of money which is down to the fact there is more than one definition for money. I decided to look in the dictionary I have:
1) (a)pieces of gold, silver, copper etc. stamped by goverment authority and used as a medium for exchange
(b) any paper note authorised to be used
2) anything used as a medium for exchange

So...using 1) we must conclude money is discrete.
But using 2), and given that apparently fractions of pennies can be electronically exchanged, this most definitely supports the continuous argument.