Irrational numbers are real numbers that cannot be expressed as a ratio of two integers. They are called irrational because they cannot be written as a simple fraction. Here are some key points to keep in mind about irrational numbers:

- Irrational numbers are infinite and non-repeating decimal numbers.
- Some examples of irrational numbers include pi, the square root of 2, and the golden ratio.
- An irrational number can be expressed as a decimal, but it will never repeat or terminate.
- Irrational numbers can be identified by attempting to write them as a simple fraction. If the number cannot be expressed as a ratio of two integers, it is irrational.
- There are an infinite number of irrational numbers, and they are denser on the number line than rational numbers.
- Irrational numbers have many applications in mathematics, including in trigonometry, calculus, and geometry.

It is important to understand that irrational numbers are not "crazy" or nonsensical; they simply cannot be written as a ratio of two integers. One way to think about irrational numbers is as numbers whose positive integer multiples never hit an integer, but these multiples come arbitrarily close to integers. Another way to think about irrational numbers is as the slope of a line that misses all other points on the integer grid in R2. 

It is also worth noting that irrational numbers can be multiplied together to result in a rational number. For example, the square root of 2 multiplied by itself is 2, a rational number.
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