Uncertainty in measurements and epsilon delta definition of a limit

[madah12]

does the epsilon delta definition of the limit connect to the uncertainty in measurements like this? like if we measure a quantity time with value a with error of + or - delta then my formula will give me v with value L +or - epsilon or is it unrelated?

 

[mathman]

It is unrelated. The simplest mathematical approach to what you are trying to do is use elementary calculus. Specifically if you know the relationship between v and t (time), you can compute dv/dt at t=a and the v error will be approximated by this derivative times the t error.

 

[madah12]

oh I see it's linear approximation right?

 

[mathman]

oh I see it's linear approximation right?

Yes.

 

[pmacias]

The epsilon delta definition of a limit and uncertainty in measurements are closely related concepts. The epsilon delta definition of a limit is a mathematical concept that helps us to understand the behavior of a function as the input values approach a specific number. In this definition, epsilon represents a small margin of error and delta represents a small change in the input value. This means that as we make our input values closer and closer to the specific number, our output values will also get closer and closer to a specific value, within the margin of error represented by epsilon.

Similarly, in measurements, we often encounter uncertainties due to various factors such as equipment limitations, human error, or external influences. These uncertainties are represented by a margin of error, typically denoted as + or - delta, which indicates the range within which the actual value may fall.

Therefore, we can see that the epsilon delta definition of a limit and uncertainty in measurements are connected in the sense that they both involve a margin of error. In fact, the epsilon delta definition of a limit can be seen as a mathematical representation of the uncertainty in measurements. Just as we use the definition to understand the behavior of a function, we can also use it to understand the behavior of a measurement as it approaches a specific value.

In summary, the epsilon delta definition of a limit and uncertainty in measurements are closely related concepts and understanding one can help us better understand the other.