For instance, is it correct to say that the number of decimals Numbers between $220$ and $289.999...$ and the number of decimal numbers between $297$ and $297.999...$ are equal? Even though the range of the former is $70$ times bigger?
2026-04-02 13:03:33.1775135013
The number of decimals numbers between different size number ranges equal?
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Consider the intervals $[a,b]$ and $[c,d]$.
The function $f:[a,b]\to[c,d]$ given by $f(x)=\big(\frac{c-d}{a-d}\big)x+\big(\frac{ad-bc}{a-b}\big)$ is a bijection.
This means that any two closed intervals are equinumerous.
Interestingly, this means all line segments contain the same number of points, irrespective of their lengths.