Hello. This is Tenfu from Seito Shijuku. You may have encountered the concepts of acceleration, velocity, and distance in physics. After all, adding acceleration equals velocity and adding velocity equals distance, right? Here we have the idea of differentiation and integration, but if we consider integration to be addition, then differentiation can be thought of as division. Integration is used to find the area under a curve such as a quadratic or cubic function, that is, the area between the curve and the x-axis.
On the other hand, differentiation calculates the tangent to a curve, that is, the slope of the curve at a certain point. If the property of adding up a certain area of an integral is an addition type, then finding the infinitesimal range of a differential can be a division type.
What I find strange here is that the addition type and division type are combined. When we think of sets in arithmetic and mathematics, we probably think of addition and subtraction, multiplication and division. Addition and division are far removed from addition and multiplication, and it is possible that differential and integral calculus also means addition and division. So, we took it one step further and asked if there was a set for multiplication and subtraction .
For example, suppose the addition type provides the expression 4+4+4. The sum is 12, so let's do division. 12/4=3 or 12/3=4. Looking at the solutions of 3 and 4, there are either three 4s, or "if you combine the three, you get 4."
If we look at the relationship between multiplication and subtraction here, if we subtract 3x4=12, we get 12-4-4=4. Or 12-3-3-3=3. In other words, 12-(3-1)x4=4, 12-3x(4-1)=3. How about applying this to 5a?
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