- #36
- 22,183
- 3,321
So, did you figure out why
[tex]\sum_{k=0}^{+\infty}{\frac{x_k}{2^k}}<1[/tex]
if one of the xk is 0?
[tex]\sum_{k=0}^{+\infty}{\frac{x_k}{2^k}}<1[/tex]
if one of the xk is 0?
Metric_Space said:Isn't it because that means the sum above is the difference of two other sums?
Metric_Space said:Would it be all entries are 1? But it wouldn't be finite...would it?
Metric_Space said:|X_k-a_k| --> 0 as k--> infinity?
Metric_Space said:x_k=1, a_k=0 or a_k=1,x_k=0 ...is that right?
Metric_Space said:Would (x_1,x_2,x_3...) = (0,1,1,...)?
Metric_Space said:balls of radius (1/2)^k have elements
with 1's starting in the kth position and 0's afterwards OR 1's in the (K+1)st position...right?
The Hamming metric is a way to measure the distance between two points in a finite set. It is commonly used in coding theory and computer science to compare strings of characters.
The Hamming metric is calculated by counting the number of positions in which two strings of characters differ. This is also known as the "Hamming distance".
Open subsets are subsets of a larger set that do not contain any of the boundary points of the larger set. In other words, they are sets that are entirely contained within another set.
In the context of proving the Hamming metric, open subsets are used to show that the Hamming distance between two points is always greater than or equal to 0. This is because open subsets do not contain any boundary points, so the Hamming distance cannot be negative.
The basis of X is a set of elements that can be used to represent all other elements in the set X. In the context of proving the Hamming metric, the basis of X is used to show that any two points in X can be represented by a finite number of elements, which is necessary for calculating the Hamming distance.