# The Number Zero

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```					From Zero to Hero

‘0’
“In the beginning was the word, but
in order to mark when the beginning
was we needed numbers.”

   History of the discovery
   Its properties and uses
   Relevance to schools
The Egyptians
   Developed civilisation
   Used maths for real life problems
   Simple number system
   Calculations were difficult and long-winded
   Therefore never came across zero
The ancient Greeks
   Accomplished mathematicians
   Better number system
   Wrote numbers in groups of ten
   HH ΔΔΔΔ III means 243

   Multiplication was hard to do
   They were no closer to discovering zero
The Babylonians
   Sexagesimal system (base 60)
   Integrated with a decimal system
   Used wedge shaped symbols written on wet clay
The Babylonians (cont…)
   Positional notation

   Started using two slanted wedges to represent a
space
The Indians
   First to consider zero as a number, and not just
a placeholder
   Put zero on the number line
Brahmagupta’s rules
   Positive + Positive = Positive
   Negative + Negative = Negative
   Positive + Negative = the difference
   If they are equal this will be zero

   Negative + 0 = Negative
   Positive + 0 = Positive
   0+0=0
Brahmagupta’s rules (cont…)
   Negative – 0 = Negative
   Positive – 0 = Positive
   For Negative – Positive
or Positive – Negative
the values should be added together
Brahmagupta’s rules (cont…)
   Negative x Positive = Negative
   Negative x Negative = Positive
   Positive x Positive = Positive
Brahmagupta’s rules (cont…)
   Positive ÷ Positive = Positive
   Negative ÷ Negative = Positive
   Positive ÷ Negative = Negative
   Negative ÷ Positive = Negative

   0÷0=0
Division by zero

   Understanding of pupils

   Bhaskara stated that n ÷ 0 = ∞

   x ÷ y → +∞ as y → 0 from positive values
   x ÷ y → -∞ as y → 0 from negative values
What is zero factorial?
nCr = n!/[k!(n-k)!]
How many ways can you pick k things from n

How many ways can you pick no things?

n!/[0!(n-0)!] = 1/0! = 1

0! = 1
What is zero to the power zero?
x0 = 1
0x = 0

So why is 00 = 1

f(x)g(x) tends to 1 as x approaches 0 from the right
f(x) = g(x) = 0
Resistance against Zero
   Reluctance to use the word ‘zero’

   Mathematicians dispute whether it’s a natural
number, even or odd

   Calendar started at 1 A.D
Relevance in schools
   Become more familiar with zero and how it can
be used
   Number and an abstract concept
   Unique but still a real number
Thank you for
listening

```
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