I uploaded this question and no one has answered because there were some flaws in the question but I have the text now. Please can some one explain how we arrive on example of line segment to have a dimension of 1.
!
Thank you
2026-02-23 19:21:08.1771874468
How to find the box counting dimension of line segment [0,1]?
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Is this your question?
To cover $[0,1]$ by segments of length $\delta$, the minimum number required is $N_\delta = \lceil 1/\delta \rceil$. This means $$ N_\delta - 1 < \frac{1}{\delta} \le N_\delta $$ and therefore $$ \frac{1}{\delta}\le N_\delta < 1 + \frac{1}{\delta} $$