What is your favorite number and why?

[Proud90sKid]

My favorite number is 1. It can be used to define all other numbers. Often, constants in equations(like the speed of light) are written as "1" to make the equations look more elegant. It represents the presence of something, which can then be used to define the absence of something (0) along with the concepts of greater whole numbers (2 is just one greater than one), their negatives, and fractions. Irrational numbers can then be represented as limits of sequences of rational numbers that were derived from the concept of 1 (3,3.1,3.14...pi) or by identifying then as cuts to the number line with all numbers less than and all other rational numbers(again, ultimately defined using 1) greater than.

The square root of negative 1 (i) is my second favorite number. It is a very weird number, but not so weird as to be be merely a mathematical curiosity. I see it when studying waves, quantum mechanics, and relativity (where it describes the time coordinate in spacetime). It appears in useful ways in these very physical equations, but the imaginary term itself always calculates itself out at the end when trying to make a physical prediction. How do they help with studying oscillations? Well, there is a beautiful formula by Euler that relates raising a number to an imaginary power to sinusoidal waves. How is that more useful than just writing a regular sine and cosine function? Because when the power has a real component, then you have exponential growth (instability) or decay (dissipation). The formula is e^(i*theta)=cos(theta) +i*sin(theta) when theta is real. If you can find circumstances in which theta or wavenumber itself has an imaginary component(thus, the total power having a real component), then you can establish the conditions in which exponential growth and decay can occur. Very amazing thing to see used in physics. Imaginary quantities aren't observable, but they are within the description of things that describe real quantities. Then there is the result in mathematics that functions that are smooth on the real line can not necessarily be uniquely described everywhere by the function's behavior at a given point, but those which are smooth across both the reals and imaginaries can be uniquely reconstructed for all points by their behavior at any single point.

[Xx_darkflameninja_xX]

7 is my favorite
lucky number 7
roll two dye and most likely its 7
the most things people can remember at a time is 7
july is the 7 and the best month
7 colors in a rainbow
7 continents
7 seas if you like pirates
thats 7 reasons why 7 is the best lol