# Search Results

Results tagged with Search options answers only user 17408
8 results

Using a computer to implement mathematics. For questions about (mathematical) optimization, (also) use the optimization tag.

First use Yuval's advice: With p = 2^32 - 5, remove all N ≥ p (the result is 0), then sort the rest, so now you have up to 1,000 numbers in sorted order from 0 to p-1. This is trivial to do by multipl …
answered Mar 10 '17 by gnasher729
Knowing the ratio r = A / B and nothing else about the numbers A and B, there is very little we can say about for example A / (B + 1) or A / (B - 1). We have A = rB. If for example B = 1, then A = r, …
answered Jun 17 '17 by gnasher729
The real numbers are uncountable. The set of real numbers that can be represented in any way is countable. Therefore, almost all real numbers cannot be represented by a computer at all. The most com …
answered Mar 22 by gnasher729
Note: You are not asked to give a list of all numbers. You are asked how many there are. A simpler question: How many integers from 1 to $10^{18}-1$ are divisible by both 2 and 3? You can figure this …
answered Jul 3 '16 by gnasher729
Counting all such numbers less than X can actually be done quite easily in $O (\log x)$ steps with a rather large constant, which would let us find the count for large values like X = $10^{100}$ quite …
answered Jul 4 '16 by gnasher729
They are among other things very useful for calculating logarithms, or square roots and cubic roots. For example: log x = log ($2^e * m$) = e * log 2 + log m. With 0.5 ≤ m ≤ 1, you can approximate l …
answered Jul 26 '17 by gnasher729
If we ignore effects of overflow and assume we can square x as often as we like in constant time, then the first example clearly either stops immediately if n ≥ 2, or runs forever if n < 2. In the s …
answered Sep 23 '18 by gnasher729
The fundamental restriction is human computer programmers' inability so far to create computers equipped with real intelligence. "Never" is a very long time, so it's hard to accept that something will …
answered Feb 14 '17 by gnasher729