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Comment by RivieraKid | Hacker News Reader

What is O(1000) satellites?

It's an unnecessary misuse of the Big O notation used to establish bounds of functions. I think they just meant up to 1000 satellites

The author means literally 1000 satellites.

It's borrowed from comp sci, but you can read O(x) as "on the order of x", so maybe 900, maybe 1200, but somewhere around there.

In Comp Sci O() notation has a very specific meaning and "on the order of" does not approximate it. I think it was probably just a misuse of the notation.

"The letter O is used because the growth rate of a function is also referred to as the order of the function"

order of...order of

yeah I know there is no "growth"

You've taken an informal and sloppy summary of big-O notation, isolated a single English expression, and construed that a similar English expression used in a different context with entirely different meaning is an accurate approximation of the formal meaning. You would be incorrect.

I have seen it getting used in many places and it's understood as order of. O(n) means at worst case number of steps needed to complete an algorithm would be c.n + a. So it is completely valid use since O(1000) would mean it can be c.1000 + a, which actually means order of 1000s.

This is also an inaccurate description of the property O().

How so?

https://www.khanacademy.org/computing/computer-science/algor...

https://en.wikipedia.org/wiki/Big_O_notation

> Big O notation is a mathematical notation that describes the limiting behavior of a function when the argument tends towards a particular value or infinity.

I.e., it's an asymptotic upper bound.

It's also interesting to compare with Ω() (Big Omega — asymptotic lower bound) and Θ() (Big Theta) (big-O AND big-Omega): https://en.wikipedia.org/wiki/Big_O_notation#Family_of_Bachm...

A good textbook on this subject is Introduction to Algorithms: https://www.amazon.com/dp/0262033844/ .

What I described is the same thing in layman's term. Worst case is the colloquial word for upper bound. And in that example n was approaching 1000.

If you want to be puritan the only fault I see in my definition is instead of using a generic function I assumed it's linear function - but that's for explaining the colloquial use.

It's just an asymptotic upper bound (though often used to imply tight bounds).

It's most commonly applied to worst case running time, but is often applied to expected running time ("hash table insertions run in O(1)"), space complexity, communication overhead, numerical accuracy and any number of other metrics.

Yep. Often people mean the narrower big-theta when they express complexity in terms of big-O.

In informal contexts it's also used as a fudge/handwave, purely as a questionable analogy that nobody is expected to take too seriously. `theptip` almost certainly knows that O(1000)=O(1), they were just being playful.

Exactly.

I guarantee you can find dozens of examples of CS-type people using O() in non-algorithmic-complexity topics as "on the order of" or "approximately" right here on HN within the past 6 months. They aren't all misusing that notation - it is being co-opted into a more general lexicon, whether you like it or not.

And I wasn't saying that "on the order of" is an approximation of what O() actually is in CS, merely that that is how OP used it.

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