Question

How many natural numbers are there between 50205 and 50225?

Answer 1

Hint: In this question, we will use the concept of natural numbers. We will use the formula x - y - 1 where x > y and solve accordingly by substituting the values of x and y.

Complete step-by-step solution -
Natural numbers are a part of the number system which includes all the positive integers from 1 till infinity. It is an integer which is always greater than zero. Natural numbers are part of real numbers. It should be noted that the natural numbers include only the positive integers, N = {1, 2, 3…. $\infty $}. Natural numbers will never consist of negative numbers or zero. Every natural number has a successor which is also a natural number. 0 is not the successor of any natural number. If the successor of x equals to successor of y, then x equals to y.
We know that,
Total natural numbers between the natural numbers x and y where y is less than x (y < x),
$ \Rightarrow T = x - y - 1$ \[ \ldots ..{\text{ }}\left( 1 \right)\]
Here,
$\begin{gathered}
   \Rightarrow x = 50225 \\
   \Rightarrow y = 50205 \\
\end{gathered} $
Substituting values of ‘x’ and ‘y’ in equation (1), we get,
$\begin{gathered}
   \Rightarrow T = x - y - 1 \\
   \Rightarrow T = 50225 - 50205 - 1 \\
   \Rightarrow T = 20 - 1 \\
\end{gathered} $
$ \Rightarrow T = 19$
Hence, between 50205 and 50225 total natural numbers = 19.

Note: On solving this type of questions, the problem faced is whether you mean ‘between’ inclusive or not. The natural numbers are (conventionally) the set containing zero, one, two, three, and so on: adding one to each natural number gives us its successor, which is also a natural number. (Some definitions of the natural numbers start with one, but this is now uncommon.). The other part of answering your problem in general requires knowing how you are representing your numbers that are inclusive or exclusive.