Albert said:given :
$\left | x-3 \right |\leq k$, and $\left | y-3 \right |\leq 2k$
prove :
$\left | x-y \right |\leq 3k$
The notation "abs(x-y)<=3k" means that the absolute value of the difference between x and y is less than or equal to 3k. In other words, the difference between x and y is between -3k and 3k, inclusive.
This proof is commonly used in various branches of science, such as mathematics, physics, and engineering. It can be used to show the relationship between two variables and their relative differences or similarities.
The number 3 in this proof serves as a constant factor that represents the maximum difference between x and y. It allows for a more precise and standardized measurement of the relationship between the two variables.
Yes, this proof can be applied to any number of variables. The notation "abs(x-y)<=3k" can be extended to include multiple variables, such as abs(x-y-z)<=3k, to represent the absolute value of the differences between all the variables being less than or equal to 3k.
This proof is closely related to the concept of tolerance, which measures the acceptable deviation or variation from a desired or expected value. The notation "abs(x-y)<=3k" sets a tolerance limit of 3k for the difference between x and y, indicating that any difference within this range is considered acceptable.