- #1
cubic
- 6
- 0
Ok so what I want to know is, is this valid? If so what does it mean?
Like mathman said, use Δx. dx has its own meaning. Δx can represent some small distance along the x-axis.cubic said:It has to be along a distance dx.
cubic said:dx is the width of each strip. dx would then be the width of the first strip. Δx is the width of a finite number of strips, which is not what I am looking for.
Infinitesimals are infinitely small numbers that are used in the process of integration to represent the area under a curve. They are typically denoted by dx and are considered to be infinitely small compared to regular numbers.
Infinitesimals are used as the limits of an interval in the process of integration. They are used to represent the width of each small interval under the curve, and as the number of intervals approaches infinity, the sum of these infinitesimals gives the exact area under the curve.
Infinitesimals play a crucial role in the process of integration as they allow us to accurately calculate the area under a curve. Without them, integration would not be possible as we would only be able to approximate the area using finite rectangles rather than finding the exact value.
No, infinitesimals are not considered to be real numbers. They are a mathematical concept that represents a quantity that is infinitely small. In the real number system, there is no number that is infinitely small, so infinitesimals are not included.
Yes, infinitesimals have applications in other areas of mathematics, such as calculus, differential equations, and non-standard analysis. They also have uses in physics, engineering, and other fields where continuous quantities are involved.