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Infinitely small does not exist

In mathematics an abstract object is defined that is called infinitely small. It is not a number, as it has no fixed value. You can perform calculations with it – if you keep that in mind.

Can you now say, that infinitely small does not exist?

 


Explanation

We normally work with the decimal numbers

1,  2,  3,  4,  5,  6,  7,  8,  9

and you can add 0 to that. You use it for writing fractions, like 1/2 and square roots, like √5. A calculation with negative numbers is possible. There are important numbers that you cannot write in all detail, and they have become names like π and e. They all have a place on the number line.

Infinitely small is not on this line, as it has no fixed value. We often use the symbol Δx or the small letter h for it. For infinitely large we use the symbool and that is also not on this line, as it has no fixed value either.

Even more strange are complex numbers, where the imaginary unit i is used. And every number is also a complex number …

Is this all just hocus pocus?

We call 7 a real number. That doesn't mean it "exists" or "is part of nature". And that applies to all these objects. Sometimes we make pictures to show the different numbers and objects. The complex plane is an example. That is quite logic and nice. It are tools.

But saying that a number exists and something infinitely small not, has no meaning at all. Mathematics is not about physical matters. There are many other sciences that deal with it, and they are equally important.

 


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