 Zero

## 04 Feb Zero

Zero is one of the most cool numbers is mathematics. The concept of zero was invented in India by Brahmagupta and this invention has been dubbed as one of the greatest advances in the history of mathematics. Zero has some unique properties and because of these properties, you have to be very careful while dealing with zero. In this article, we are going to take a look at some of those unique properties of zero that you will not in a typical math tuition class.

Multiplication with Zero
As mentioned above, zero has some unique properties of its own. We know what happens when we add to or subtract from zero. If you add some number to zero or subtract zero from some number, the number remains the same. Astonishingly, when any number is multiplied with zero, the result is always zero. Have you ever wondered why? Some of might already know the answer. Nevertheless, let us see why this is the case.

To understand why it is like the way it is, we must first understand the operation multiplication. What is multiplication? In fact, it is actually a slightly different form of addition. For example, let us consider the following:

2+2+2+2=8
In the above equation, we can see that when we add four 2s, the result is 8. Thus your maths tuition teacher can say that four 2s make 8 and can write it in the following way as well:
2 x 4 =8

By using the same line of reasoning, your maths tuition teacher could say that eight 5s make 40, four 3s make 12 and so on. Now in case of zero, it does not matter how many number of zeros we add, we will always have zero as our answer. In other words, it does not matter whether we have 15 zeros or 10,000 zeros- the answer will always be zero. As a result, your maths tuition teacher will tell you, any number, whenever multiplied by zero, always yields zero.

Division by Zero
So, as your maths tuition teacher has already taught you how zero interacts with the three basic arithmetic operations – addition, subtraction and multiplication. However, division with zero is tricky. To be frank, division by zero is simply not allowed in mathematics and the result is known to be ‘undefined’ when any number is divided by zero. What does it mean when we mention the result of dividing by zero is undefined? The phrase ‘undefined’ simply highlights the fact that ‘we do not know’ what happens when we divide by zero.

(It is important to mention here that there is a common misconception that the result of dividing by zero is ‘infinity’, which is not correct.)

Is zero an even number?
This is a tricky one or is it? Have you ever thought about it before or asked this to your maths tuition teacher in your math tuition class? Before reading on, please take a moment to think about it. Zero is actually an even number and it satisfies all the properties of an even number. An even number is a multiple of zero and zero satisfies that condition as 2 x 0 = 0. Next, an even number should always sit between two odd integers and 0 does that. If we take a look at the number line, we will see that 0 sits between -1 and 1, both of which are odd. Finally, any even number, when added to an even number will always yield an even number as the result. Zero satisfies this condition as well. Add 0 to any even number and the result you get is the even number that you added with zero itself. Hence, zero is considered to be an even number.