Dick said:The point is a_{ij}>i*j. You will run out of numbers at a finite point even if a_{ij} gets to be hugely large. It's not really a Cantor problem. The index set is the limit.
The notation n^2 refers to the number of elements in an array when it is squared, while 8*n refers to the number of elements in an array multiplied by 8. This means that n^2 is a quadratic relationship, while 8*n is a linear relationship.
In general, 8*n is more efficient than n^2 in terms of array operations. This is because linear relationships have a lower computational complexity compared to quadratic relationships, meaning that operations on arrays with 8*n elements will take less time and resources compared to arrays with n^2 elements.
The size of an array can be represented by either n or n^2, depending on the dimensionality of the array. For example, a 1-dimensional array of length n will have n^2 elements, while a 2-dimensional array with n rows and n columns will have n^2 elements. Similarly, an array with 8*n elements can be interpreted as having a size of n or n/8, depending on the dimensionality of the array.
n^2 would be more useful than 8*n when dealing with operations that require the array elements to be accessed or manipulated in a quadratic manner. For example, if a problem requires finding all possible combinations of elements in an array, n^2 would be a more appropriate representation of the array size rather than 8*n.
By understanding the relationship between n^2 and 8*n, developers can make informed decisions about the size of arrays and the operations performed on them. For example, if a problem requires a large number of array operations, using an array with 8*n elements rather than n^2 elements can significantly improve the efficiency and speed of the code. This understanding can also assist in identifying potential bottlenecks and optimizing code for better performance.