Introduction
The number system is a fundamental concept in mathematics. It is the study of numbers and their properties. The number system is classified into different categories such as natural numbers, whole numbers, integers, rational numbers, and irrational numbers. In this response, we will focus on irrational numbers and how to find an irrational number between 1.02345 and 2.02345.

Irrational Numbers
An irrational number is a real number that cannot be expressed as a ratio of two integers. Irrational numbers are non-repeating, non-terminating decimals. Some examples of irrational numbers are √2, √3, π, and e.

Finding an Irrational Number between 1.02345 and 2.02345
To find an irrational number between 1.02345 and 2.02345, we can use the decimal expansion of an irrational number. One such irrational number is √2, which is approximately 1.41421356.

Now, we can use this approximation to find an irrational number between 1.02345 and 2.02345. We can add this approximation to 1 and subtract it from 2 to get the range between which we need to find an irrational number.

1 + √2 and 2 - √2 are both irrational numbers that lie between 1.02345 and 2.02345.

Therefore, an irrational number between 1.02345 and 2.02345 can be:

1.02345 + (2 - √2 - 1.02345)/2 = 1.6875

Conclusion
In conclusion, the number system is a fundamental concept in mathematics, and it is classified into different categories. An irrational number is a real number that cannot be expressed as a ratio of two integers. To find an irrational number between 1.02345 and 2.02345, we can use the decimal expansion of an irrational number such as √2. By adding and subtracting the approximation of √2, we can find an irrational number that lies between 1.02345 and 2.02345.

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