Mathematics is a way of describing the world around us and finding relationships between things that we can see and things that we can’t. These relationships are not a result of the way our system is set up. How we define components of the relationships would be different, but the fact that they exist would not change. When examining two items, they can be equal or not equal. That is not dependent on the system that we have created to look at mathematics.

Our numbering system is built around a base ten system. Nothing would change if we used a number system that was modulo 3, 6, or 986. The fact that 2+2=4 would still hold and the fact that the net force of a system is equal to mass times acceleration would still be true. We may not use those words or those symbols, but the relationships would still be the same.

This is one of my favorite images depicting the purity of mathematics. It is the best way that we have found to describe the universe. It seems impossible to perform any task without the use of mathematics. You car’s ability to start is a result of numerous mathematical calculations used to determine the specifications for all of the parts that are required to start your engine. Figuring out how much food to buy when you are at the grocery store requires you to figure out how many meals you need to feed a certain number of people for a specific number of days. Determining the concentration of sodium in a solution requires a variety of calculations.

All of those problems would still be solvable regardless of how we define our numbering system and finding these solutions would still be mathematics. Math is not so much about what a single number represents or what the final answer is, as much as it is about that consequences that follow from arriving at that answer. If the way we had defined our numbering system lead to the answer that you needed to purchase x amount of food, or if a different numbering system lead to the answer that you needed to purchase y amount of food, the consequences are the same. Either way, you used math to feed your family for the week.

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coherent: I’m not sure how your first half about numbers and 2nd half about applications of math tie together. Maybe adding a conclusion (consolidation) that ties it together from your point of view would unite the halves.

content, complete-ish, clear: +

Plus one of the best mathcomics ever, of course.