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.