4 ms·

Not really relevant to the discussion, but O(10) doesn't mean "approximately 10". O(f(x)) denotes a function that is bounded by a constant multiple of f(x), an

Not really relevant to the discussion, but O(10) doesn't mean "approximately 10". O(f(x)) denotes a function that is bounded by a constant multiple of f(x), and really only makes sense in the context of a dependent variable x. (e.g. O(2^x) denotes an exponential-bounded relationship with x). So O(10) in the above context effectively means your apartment uses some unknown number of kWh.

dhimes 12y ago
When dealing with numbers, the notation means "order of magnitude," which is the nearest power of 10. Strictly, this places is between 5 and 50 (4 rounds down to 1, 51 rounds up to 100). Most people use it a little more loosely in conversation. More than 1, not 100, etc.
- stcredzero 12y ago
  I didn't know this. I'm used to just talking about "order of magnitude."
- dllthomas 12y ago
  While I've occasionally seen O(...) used to mean "approximate upper bound" or even "approximate bound" in a more general way than the math for Big-O notation would permit, I've assumed it was either error or analogy, not a specific other function. Can you give a citation for this being an established usage? (Note that I'm certainly familiar with orders of magnitude, just not this notation for them.)
  - dhimes 12y ago
    It may be informal. I seem to recall people also using ~ for this, as in "The detector is measuring eV, but this effect is ~ meV |O(meV) so we won't see it."
stcredzero 12y ago
To expand on this: O(10) is the same as O(9) or O(1) and O(k). (k is a constant) Key to understanding this: Note that if you graphed out all the above as functions, they would all be horizontal lines. O is about the kind of function something is, specifically relating to how fast it expands.
Tarrosion 12y ago
You are completely correct, of course. At best it's an abuse of notation and perhaps an abuse of idea. But hopefully a fairly readable abuse! I don't know a better shorthand for "of approximately the same order of magnitude." There's ~, but it also has its problems...if I say "I am ~175cm tall," I am not allowing for the possibility that I am 100cm tall or 500cm tall. Is there an established convention?
- ksenzee 12y ago
  I don't know of an established convention. I've heard people just say "within an order of magnitude." This may be a readable abuse to some, but not all; when I saw O(10) I just saw a horizontal line graph in my head and thought "huh?"

dhimes 12y ago

When dealing with numbers, the notation means "order of magnitude," which is the nearest power of 10. Strictly, this places is between 5 and 50 (4 rounds down to 1, 51 rounds up to 100). Most people use it a little more loosely in conversation. More than 1, not 100, etc.

stcredzero 12y ago
I didn't know this. I'm used to just talking about "order of magnitude."
dllthomas 12y ago
While I've occasionally seen O(...) used to mean "approximate upper bound" or even "approximate bound" in a more general way than the math for Big-O notation would permit, I've assumed it was either error or analogy, not a specific other function. Can you give a citation for this being an established usage? (Note that I'm certainly familiar with orders of magnitude, just not this notation for them.)
- dhimes 12y ago
  It may be informal. I seem to recall people also using ~ for this, as in "The detector is measuring eV, but this effect is ~ meV |O(meV) so we won't see it."

stcredzero 12y ago

To expand on this: O(10) is the same as O(9) or O(1) and O(k). (k is a constant) Key to understanding this: Note that if you graphed out all the above as functions, they would all be horizontal lines. O is about the kind of function something is, specifically relating to how fast it expands.

Tarrosion 12y ago

You are completely correct, of course. At best it's an abuse of notation and perhaps an abuse of idea. But hopefully a fairly readable abuse! I don't know a better shorthand for "of approximately the same order of magnitude." There's ~, but it also has its problems...if I say "I am ~175cm tall," I am not allowing for the possibility that I am 100cm tall or 500cm tall. Is there an established convention?

ksenzee 12y ago
I don't know of an established convention. I've heard people just say "within an order of magnitude." This may be a readable abuse to some, but not all; when I saw O(10) I just saw a horizontal line graph in my head and thought "huh?"