So is an alternative way of writing, meaning that can take any value from 2 to 7, including 7 but not including 2. A round bracket indicates an exclusive inequality and a square one is inclusive. 1.20 to 1.23 Inclusive and exclusive inequalitiesįinally (for this section) we have an alternative form of mathematical notation used to indicate inclusive and exclusive inequalities. On the other hand, if had to be either less than or equal to 2, or greater than 7 (and of course couldn’t be both at the same time), then you’d use the (union or OR) symbol and write It’s implied that is a real number, so you can usually omit, but if it has to be an integer then you should include that too: Which alternatively could be written using the (intersect or AND) symbol as You’d normally write this solution as but in set notation it would look like this: Let’s say you’ve solved your inequality and found that has to be greater than 2 and less than or equal to 7. If you’re asked to give the answer to an inequality question using set notation then this is the form of mathematical notation that you should use. 4.7 is a rational number (it can be written as, for example, ) but not an integer. Īnd the symbol indicates membership of a set: but, i.e. The relationship between and is equivalent to the relationship between the exclusive inequality and the inclusive one. In fact it also goes the other way – all positive integers are natural numbers – so you could just use instead of. It could also be said that : All natural numbers are positive integers. all integers are real, but not all real numbers are integers. – the set of integers is a proper subset of the set of real numbers, i.e. We can use the symbols 1.1 to 1.4 to show the relationships between the sets. (Some definitions of include zero but the English A-level doesn’t.) This is exactly the same as the set of positive integers. It can be modified by adding a superscript “+” to specify the inclusion of only positive values, and a subscript “0” to include 0 as well. whole numbers, including zero and negative integers. For example, is a rational number sometimes used as an approximation for π, which is irrational. Think of it as Q for Quotient the quotient is what you get when you divide one value by another. Is the set of rational numbers: numbers that can be written as a ratio or fraction, i.e. If you study Further Maths at A-level then you’ll also be dealing with imaginary numbers (where the imaginary number ), but you don’t need to worry about those for the single A-level. This covers all the numbers that you’ll be dealing with in A-level Maths. Is the set of real numbers – in other words any number that doesn’t involve the square root of a negative value. Let’s start with the mathematical notation for different number types. 1.1 to 1.4 and 1.11 to 1.15 Number types and relationships It’s likely that you’ll have come across some set notation at GCSE, such as the union and intersect symbols, and listing the members of a set enclosed in curly brackets, but there are more symbols you need to understand. Part 3: Vectors, Statistics and Mechanics Set notation This article covers set notation and miscellaneous symbols that don’t fit into any other category. The images used here are taken from the Edexcel spec, but the list is the same for all. You can find an exhaustive list in the appendices to the specification published by your exam board – Edexcel (9MA0), AQA (7357), OCR (H240) and OCR/MEI (H640) – but I’m going to provide a little more explanation for the ones that you’re most likely to come across. Much of the mathematical notation that you need to know for A-level, you’ll already have come across at GCSE, but there are some symbols that you may not be familiar with and others that you certainly won’t have used before studying Maths at A-level.
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