[Maths Class Notes] on Zero Pdf for Exam

All the list of whole numbers is the part of integers that starts with zero and ends at infinity. Since we know integers are the numbers that can be produced by adding and subtracting one’s together.

Suppose, if we add 1 + 1, we get 2, which is an integer.

In the same way, if we subtract 1 from 1, we get 0,

1 – 1 = 0

Therefore, 0 is a whole number.

0 as a Number

• 0 is the integer that precedes the positive number one and follows the number −1. In most of the numerical systems, 0 was identified even before the idea of ‘negative integers’ was accepted.

• Zero is an integer that quantifies a count or an amount of null size; that is, if the number of your brothers is equal to zero, this means the same thing as having no brothers.

• And if something has a weight equal to zero, it means it has no weight.

• If the difference between the number of pieces in two piles is equal to zero, it means the two piles have an equal number of pieces. Even before counting starts, the result can be assumed to be equal to zero; that is the number of items counted before you count the first item, and counting the first item brings the result equal to one. And if there are no items to be counted, the number zero remains the final result.

While all mathematicians accept 0 as a number, some non-mathematicians would say that zero is not a number, arguing one cannot have 0 of something. Others hold that if suppose you have a bank balance of zero rupees, you have a specific quantity of money in your account, that is namely none. It is that latter view that is accepted by mathematicians.

Almost all historians omit the year zero from the proleptic Gregorian and Julian calendars, but astronomers include it in these same calendars. However, the phrase Year Zero can be used to describe or demonstrate any event considered so significant that it virtually starts a new time reckoning.

Zero as a Decimal Digit

Positional notation without the use of zero (using an empty space in tabular arrangements, or the word kha which means “emptiness”) is known to have been in use in India from the 6th century. The earliest certain use of zero as a decimal positional digit date to the 9th century. The glyph for the zero digits was written in the shape of a dot, and consequently called Bindu “dot”.

The Number Zero

Zero shows that there is no amount. Example: 6 − 6 equals 0 (the difference between six and six is zero). The number zero is also used as a “placeholder” so we can write a numeral properly.

Example: 502 (five hundred and two) could be mistaken for 52 (fifty-two) without the zero in the tens place.

Zero is a Very Special Number

It is halfway between the number −1 and number +1 on the Mathematics Number Line: Zero is neither a negative number nor a positive number. But zero is an even number.

The Idea of Number Zero

The idea of zero, though natural to us now, was not natural to early humans. if there is nothing to count, how can we count it?

Example: You can count dogs, but you can’t count an empty space:

(Images will be uploaded soon)

Zero as a Placeholder

About 3,000 years ago when people needed to tell the difference between numbers like number 4 and the number 40. Without zero, they both look the same!

So zero is now used as a “placeholder”: it shows “there is no number at this place”, like this:

602 – This means 6 hundred, no tens, and 2 ones.

The Value of Zero

Then people started thinking of zero (0) as an actual number.

Example:

“Let’s say, I had 3 oranges, then I ate all the 3 oranges, now I have zero oranges…!”

Additive Identity

And zero has a special property: when we add it to a number we get that number back, unchanged.

Example:

7 + 0 = 7

Adding 0 to 7 gives the answer 7

Also 0 + 7 = 7

This makes it the Additive Identity, which is just a special way of saying “add 0 and we get the identical (same) number we started with”.

Here are some of zero’s properties:

Special Properties