# Tag Info

Accepted

### How does a computer interpret real numbers?

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 ...
Accepted

### Is it possible to accurately determine the number of instructions required to multiply or add two integers in a modern processor?

Yes and no. “Instructions” isn't the right unit of measure: most processors include an ALU and require a single instruction to perform addition or multiplication on a number of a certain size (...
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### Is it possible to make a language that can build upon itself perfectly?

Interesting that you reflect on this issue. This is very similar to the issues that I was reflecting on when I started my Phd research back in 1976. Back then Extensible Languages were very in vogue. ...
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### Good resources for understanding semidefinite relaxation for combinatorial problems

The Design of Approximation Algorithms by David P. Williamson and David B. Shmoys is an excellent handbook on approximation algorithms. It has an entire chapter devoted to the topic of SDPs. As of now ...
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### Solving for the matrix $W$ in an equation involving $W \cdot W^{T}$

You might be looking for the Cholesky decomposition. The referenced article also contains an example for $M$ having negative entries. Note the constraints on $M$ for this decomposition to exist.
Accepted

### Can a computer count to infinity?

It depends on what you mean by "count to infinity". Specifically, how does the computer give output? consider the following quesitons: Can a computer show, on its screen, all the number from 1 till (...
There is an algorithm due to Coppersmith (later improved by him) that can multiply an $N \times N^\alpha$ matrix by an $N^\alpha \times N$ matrix in time $\tilde{O}(N^2)$ for some $\alpha > 0$. The ...
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 ...