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There are many aspects here:
* You simply use it (in interactive mode)
* You integrate it into your application as static lib
* You integrate it into your application as a dynamically linked lib
* You use it via some kind of (remote) API
* Do you integrate via source code, static lib, dynamic lib, API
Is there any non-syntactic difference between these two lines?
JMP Ox1234
GOTO label_1234
I think they are identical and the question is only where target labels can reside, how they are represented, and when the jumps are triggered (operation).- Introduce scopes and program structure instead of explicit labels (instruction addresses) and using control flow operators which rely on this structure
- Procedures and procedure calls
- Overriding and virtual functions where the system knows how to find the next instruction to jump to
- Concurrency and multi-threading where resume operation means essentially jumping to some (dynamic, not static) instruction address.
- Asynchronous and even-driven programming
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However,
SELECT a1,a2,... FROM Table AS t WHERE Condition
is syntactically equivalent to Python list comprehension: [(t.a1,t.a2,...) for t in Table if Condition]
Here the use of attributes (SELECT) is also written before the iterator.SELECT is also analogous to normal loops:
foreach t in Table
if not Condition: continue
# Use t.a1, t.a2 etc.
Here we first provide the loop specification while the usage of elements is written only in the body.0 = nothing = non-existence.
This statement reduces the problem to the definitions of "existence" and "physical reality" which of course may have quite different interpretations. For example, the existence of particles (with finite mass and finite coordinates which can be "touched") and the existence of waves are rather different notions.
The possibility to provide arbitrary data processing functions is one of the core features of contemporary query languages. In SQL it has always been a huge problem (and your example is a good demonstration). In the example provided by they also rely on a built-in (exponential smoothing) function and therefore it is not clear whether I can really perform arbitrary ad-hoc computations within the query itself (without built-in or externally defined functions).
"Userful way of thinking" and "analyse" something is not a real object strictly speaking - it is a process or phenomenon (no doubt complex numbers are useful here).
But can you say what kind of real object or property a complex number represents or measures? For example, an integer can represent the number of apples and their weight is represented by a real number. What property of a real object can be expressed, for example, as 50i ?
What people complain about is that they do not have a (real or hypothetical) device which can display its measurements as a complex number while they do have devices which measure properties in terms of integer, rational and real numbers.
If by reality we mean the real world (not mathematics or some abstract model) then the article does not actually answer the question what the complex numbers are really -- they describe what complex numbers mean mathematically (geometrically, algebraically, number theory).
Here are some interpretations of imaginary and real parts in terms of the real (physical) world:
o Time vs. space. This means that they have to be measured using different constituents with different properties. For example, space is reversible and periodic (we can return to the same point where we were before many times while it is not possible to return to previous point in time).
o Periodic vs. monotonic behavior. For example, rotation frequencies or oscillators (electric or physical) vs. linear motion.
Yes, if it exists (as an element of some set), then it is definitely outside the declared set of values. The main question is how we can formalize it, particularly, by defining the set NULL is a member of. For example, the following general approaches are possible:
o Extend (any or some) set of values with a special element (NULL)
o NULL = 0 (empty set)
o NULL = <> (empty tuple)
o Treat NULL as non-existence which entails having no-op if it is met, for example, 2 + NULL + 3 = 5 (just delete NULL which means skip it).
It is known to be one of the major controversies because originally NULL means the absence of a value which entails that it is not a value. Hence, if there are no values, then we cannot do any operations. Yet, for whatever reason (avoiding exceptions etc.) expressions with NULL need to be evaluated and hence NULL is treated as a value. So we get a problem: NULL is not a value AND NULL is a value. There are different views on this problem and the solution implemented in SQL (and three-valued logic) is probably not the best one.