# Member Work: Number Sets for Toddlers

Member Ross Sweet used the Lead CNC machine to make a series of toddler tray puzzles. Mathematics fans may recognize the characters – for the rest of us, it’s the common number sets!

• N – the natural numbers, which are the numbers we use for counting (1, 2, 3, etc) The natural numbers are a subset of…
• Z – the integers, aka. numbers that don’t have a fractional component. They also include the negative numbers (-1, 0, 1, 2, 3, etc). The integers are a subset of…
• Q – the rational numbers, aka. numbers that can be expressed as a fraction. For example, -3/7 is a rational number because it can be expressed as a fraction. Another example would be: 3/1 (one way you can write ‘3’ as a fraction). The rational numbers are a subset of…
• R – the real numbers, which consist of every point on the number line. Remember pi (π)? It can’t be written as a fraction, so it’s not rational. It is infinitely long, but it’s also on the number line, so it’s real! You might think that’s the end, but the real numbers are themselves a subset of…
• C – the complex numbers! These numbers include the imaginary unit i. I is defined to be the square root of negative one. Complex numbers are written as a + b*i (where ‘a’ and ‘b’ are real numbers). The real numbers are a subset of the complex numbers, because you can write the real numbers as complex. For example, 6+0i is equal to 6. Clear as a lead window, right?

Complex numbers were first conceived around 1545 by italian mathematician Gerolamo Cardano. And even though he invented them, like most of us he thought they were pretty much useless. Other mathematicians continued to develop the idea of complex numbers, but it wasn’t until the 20th century that they found practical applications in the real world. Complex numbers are used in signal analysis, electrical engineering, fluid dynamics, quantum mechanics, just to name a few. (Continue down this internet rabbit hole on Wikipedia.)

Best complex numbers explanation I found on the Interwebs:

Imagine an electronic piano. Each key produces a different tone. A volume control changes the amplitude (volume) of all the keys by the same amount. That’s how real numbers affect signals.

Now, imagine a filter. It makes some keys sound louder and some keys sound softer, depending on their frequencies. That’s complex numbers — they allow an “extra dimension” of calculation.

Copy & pasted from a post on Stack Exchange – https://math.stackexchange.com/questions/285520/where-exactly-are-complex-numbers-used-in-the-real-world

Where were we? Oh, right! toddler puzzles! People make all kinds of extraordinary things here at Area 515.