 Bournemouth Maths Tutor Barney M-T What does “MATH ERROR” mean?

SHORT ANSWER: this means you have just asked the calculator to do a sum it doesn’t like. The three most common reasons for getting this error message are: 1) you have tried to divide by zero: forbidden in maths! If you type in $3\div 0$ you are asking the calculator “zero times by what equals WHAT’S ZERO TIMES BY INFINITY?

SHORT ANSWER: 0 x ∞ = anything you like! Intrigued? Read on… LONG ANSWER: the question seems absurd: after all, zero multiplied by anything is zero, yet any multiple of infinity is always infinity. But 0 x ∞ cannot be both zero and infinity, can it? Infinity doesn’t behave in the same way as other Strange but True: IRRATIONAL NUMBERS

The first numbers we discover in childhood are the Natural Numbers: 1, 2, 3, … Next come the Integers (whole numbers) – which also include Zero and the negatives: … -3, -2, -1, 0, 1, 2, 3, … Next up: it’s fractions such as: 0.5, 2.90909… , $-\Large{5}\frac{7}{8}$ Numbers like these are said to be Here I am at the World’s Steepest Road in Harlech, North Wales. The road sign indicates an almighty 40% – but how is this measured? ON ROADS: The 40% means that however far you travel horizontally, you travel 40% of that vertically. So if you go 100m across, you go 40m up. SO A ROAD (or: Much ado about Nothing) Zero doesn’t actually exist. Think about it: by definition it isn’t anything, it’s nothing!! Even so, here are 5 facts every mathematician should know about Zero: WHICH ARE BETTER: FRACTIONS OR DECIMALS?

DECIMALS ARE WAAAY BETTER THAN FRACTIONS: most GCSE students prefer decimals because they allow you to compare the sizes of two numbers at a glance! For instance, which is bigger out of $\frac{2}{5}$ and $\frac{3}{7}$? Um…? But in decimal form we can easily see that $\frac{3}{7}=0.428571…>0.4=\frac{2}{5}$. FRACTIONS RULE SUPREME: fractions allow for easy multiplication, and QUOTE OF THE WEEK: “God Made the Integers. All Else is the Work of Man”

… or so thought Leopold Kronecker (1823-1891) in his famous quote. WHY KRONECKER WAS WRONG: the integers (whole numbers) include the Positive Integers or “counting numbers” 1, 2, 3, 4 and so on: easy for a child to understand. We could quite reasonably argue they are “made by God”. But the integers also include zero, FACTORIALS!

Factorials are so cool that the notation is: AN EXCLAMATION MARK!!!! The exclamation mark means something very specific in maths. It’s great to be impressed with numbers, but please do not put an exclamation mark after a number just to show that it’s really cool. WHAT IS IT? n Factorial (written $n!$) means the product WORD OF THE WEEK: INDEX

INDEX (plural indices): you can see these in expressions like $5^2 = 25$. The 5 is called the BASE, the 2 is called the EXPONENT or INDEX, and the 25 is called a power (in this case it’s a power of 5).