Infinity (∞) Is NOT The Biggest Number

Introduction

You think that Infinite or Infinity or whatever that thing is, is the biggest number in the world. Well, if you think that way, you were certainly incorrect. How? Let's see how.

What is a Number?

First of all, what is a number? Well, what "is" a number? It is actually difficult to define but easy to explain. Say there are a few chocolates lying in front of you. And you want to keep them with you. Now in order not to let your friend steal it from you, you need to make sure that you have the same amount of chocolates with you that you had taken earlier. But now, how will you do that? Simple, by "counting" them.

And we all know how to count right? One, Two, Three, Four and so on. So the words that you pronounce while counting something is a number, which is basically an arithmetical value. Numbers can be expressed by words, symbol, drawings etc. Numbers represent a certain quantity and are used in calculations.

Number Systems

So now, we know what are numbers. Now based on how you count or how you use them for calculations, numbers are divided into a lot of categories. Let's have a glance.

1) Natural Numbers: These are numbers that we use for counting. They come naturally to our mind while we count objects. Like, we say 1 pencil, 2 pencils, 3 pencils etc. instead of saying 0 pencil, 1 pencil etc. Because we know that is incorrect as it seems inappropriate and it seems more "naturalistic" when we start counting from 1. Examples of natural numbers include: 1, 2, 3, 4....and so on till infinity.

2) Whole Numbers: These are just the same as natural numbers but here in this case, there is a "0" (zero) added in the list. Simply put, whole numbers are a group of natural numbers but with a zero included. These numbers represent themselves as wholes. Eg.: 0, 1, 2, 3....and so on till infinity.

3) Integers: Just put a mirror and you're done! Yeah, seriously. Integers are a set of whole numbers plus the negative numbers. On a number line if you go the left side of 0, you'll start getting numbers like -1, -2, -3...and so on. So but remember integers are a collection of whole numbers and negative numbers. Both. For reference, here is a, integral number line.

4) Rational Numbers: Perfect definition: Any number of the form p/q is a rational number. Now, these numbers are actually the collection of fractions, decimals and integers. But wait, what are fractions and decimals? Simple numbers like "half, quarter, three-fourth" can not be represented on an integral number line, as you can see it clearly. Therefore there are a different set of numbers known as fractions and decimals that are used to represent them. They are very useful in dealing with problems in daily life. Sharing your chocolate with your friend uses the concept of fractions and decimals. And the total collection of all these integers (which are again a collection of whole numbers and negatives) and fractions and decimals, we get what's known as the Rational Numbers. Eg.: 0, 54, 1/2, 0.534, -234 etc.

5) Irrational Numbers: Not done yet! It seems that ancient mathematicians figured out some unique numbers that scared them! Yes, seriously. They named them irrational numbers. True to their name, irrational numbers cannot be represented in a fractional format. Rational numbers can be represented as a numerator divided by a denominator. Eg: 1/2, 6/6, 7/1 etc. But irrationals like √2, √5 etc. are incomprehensible. They can be represented on a number line and their are actually very unique ways to do it but for now we'll move ahead.

6) Real Numbers: These are the final set of numbers which are a collection of rational and irrational numbers. That's it! Now I agree there are a lot more other types of categories but these 6 are the main ones.

What is Infinity?

Okay, so we now do know a lot about numbers and their types. But now what? What is infinity? Well it turns out, that defining infinity is even more hard than defining what a number is. Infinity can be said to be successor of any big "number" that you can think off and is represented by the symbol "∞". Like say you think that 1 quadrillion (1 followed by 15 zeroes) is the largest number on Earth. Just assume that. Then according to the definition of infinity, the successor of 1 quadrillion will be 1,000,000,000,000,001. Hence it is clear why infinity is told be the biggest number. But we know that number is a constant value. It is not a variable. If I say a number 4, it will remain 4 and it will not become 3 on its own, because it is a constant.

Does that mean infinity is a variable? Well, in one sense, you can say that because infinity seems to be changing its value even if we think off the largest numbers that our brain could comprehend. So, if a number be represented by "n", then infinity will be "n+1". But that would also be a constant, that is why it is difficult to say whether infinity is a number or a constant.

Infinity has this reputation to be known as the biggest number. If you were asked to tell how many numbers are present between 2 and 3, then what would your answer be? Infinity? Yeah right? Because you can write the solution as 2.1, 2.11, 2.111 and they still count as numbers as they can be represented in the form of p/q but they are definitely not infinity. If we keep counting these numbers on and on as in how many numbers are in between 2 and 3, we'll never stop nor the numbers would end. That is what's called infinity. Therefore, infinity is not the biggest number but is a concept. That's what you need to realize.

When somebody is asked what is the largest or the biggest number on Earth, they'll just boringly say infinity, but the real answer is nothing! There is no number that is the greatest. And lastly, this question doesn't even make any sense at all! It's like asking how big is the universe, or who created the universe? It just doesn't make any sense right? And if infinity is the biggest number, then what about 1/∞? Will it be zero? No right, because it will be a very small amount. 1/∞ leads to zero but is never equal to zero. And that's the difference you need to understand.

Conclusion

Now you know that the question that what is the biggest number in the universe itself is senseless, therefore the biggest number in the universe is nothing as there is no biggest number. Any number, seriously any number you say is not the greatest. There is always a number greater than that. In fact a lot. So now don't go ahead and answer someone that the biggest number is ∞ and the smallest number is -∞. No no no! That is all wrong as you now know that infinity (∞) is a concept and not a number.

FACT: Infinity's symbol (∞) looks like a loop, isn't it? True to that, as the loop never ends, infinity also never ends. But now we know that it is not a number! Amazing right?

And now I hope that you feel better at this crazy concept of infinity and now you know the misconception as well. 

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Thank you for learning something new!