Step Function?


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I have never seen this notation for a (generic) step function. This page (https://mathbitsnotebook.com/Algebra1/FunctionGraphs/FNGTypePiecewise.html ) claims that the double bracket [[x]] is sometimes used to denote a specific step function -- the "greatest integer" function (FLOOR() function in most programming languages). Wikipedia also mentions this notation (https://en.wikipedia.org/wiki/Floor_and_ceiling_functions ), referencing this page: http://www.mathwords.com/f/floor_function.htm Wolfram does not seem to like this kind of notation, as they prefer to use different notation for floor and ceiling, which combine to make nearest integer. http://mathworld.wolfram.com/FloorFunction.html

Not sure that explains why the double brackets or anything else, but maybe it helps see that this is one way to express this particular step function, even if it is not universally accepted.

Edited by MrShorty
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I'm a historian, not a Mathematician, and there's a very good reason for that.

In layman's terms, I understand the double Bracket to mean [[x]]

as follows.

It can be used to differentiate or clear up any ambiguity between what is in a parenthesis and the other function, thus if there are two functions, even if equal it would be f(x) = [[x]] thus also could be showing an extension (beyond what the normal brackets are [as indicated in this statement in English [but who knows] are] in normal functions).

It can also be a substitute for the brackets themselves in certain situations.

Normally it is used to show that the integer should be rounded down to the greatest integer that is x or lower than x.

In this situation though, the author should have clarified what the notation is.

PS: Remember though, I'm a historian, NOT a mathematician (and thus not to truly be trusted with math [for as with false prophets [we will invariably lead you astray] who give you false teachings] because we really might not understand it all that well, which is why we are historians and not mathematicians).

Edited by JohnsonJones
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6 hours ago, Carborendum said:

My daughter just stumped me in math.  Rather her teacher did.

f(x) = [[x]]

This is apparently a method of notating a step function.  I've never seen it before.  Anyone?  Why double brackets?

You sure it's not f(x) = ||x||? I have seen double verticals used as he scalar value of a vector. So ||F|| would be notated as F, and e.g. for a 3-D vector would be √(Fx2 + Fy2 + Fz2). I have also seen double verticals sometimes used for absolute value.

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6 hours ago, Carborendum said:

My daughter just stumped me in math.  Rather her teacher did.

f(x) = [[x]]

This is apparently a method of notating a step function.  I've never seen it before.  Anyone?  Why double brackets?

https://study.com/academy/lesson/step-function-definition-equation-examples.html

It appears they aren't brackets, but "max" or "min" indiators that tell you to round down or up to the nearest integer to produce a step function.

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I've seen it. It isn't uncommon notation. I don't like it, however, as it can be ambiguous next to brackets used for delimiting expressions. It also doesn't provide a clear variant for defining the step function that rounds up to the next larger integer.

But it is accepted and valid, when properly defined.

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4 minutes ago, MarginOfError said:

But it is accepted and valid, when properly defined.

That's just it.  It was never discussed in class.  And they have no textbook.  It just showed up in a homework assignment.  She decided to ask her engineer father.  And I was stumped.  I was familiar with step functions.  But I've never seen it notated in this manner.

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1 minute ago, Carborendum said:

That's just it.  It was never discussed in class.  And they have no textbook.  It just showed up in a homework assignment.  She decided to ask her engineer father.  And I was stumped.  I was familiar with step functions.  But I've never seen it notated in this manner.

That's just sloppy mathematics. Welcome to the field. :)

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3 hours ago, Vort said:

https://study.com/academy/lesson/step-function-definition-equation-examples.html

It appears they aren't brackets, but "max" or "min" indiators that tell you to round down or up to the nearest integer to produce a step function.

Thanks.  I did eventually look it up.  But it took adept level Google-ocity.  It was beyond my daughter's ability to look it up.

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7 hours ago, bytebear said:

Wait until she gets a European teacher, and then you have to deal with commas uses as periods and periods as commas and the minus sign is the backslash. Ugh, I hated that teacher.

She's already come across that.  It's spinning her brain.

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On 9/23/2018 at 9:27 AM, Sunday21 said:

It is very common here, Ontario, to hire a math tutor when your child goes through high school. This tendency causes me to wonder about the level of math instruction in high schools.

We refused to allow our children to take math in high school, even if they wanted to do public schooling (which they all chose to do, to some extent). No math. Math teaching sucks. We kept the math teaching at home.

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28 minutes ago, Vort said:

We refused to allow our children to take math in high school, even if they wanted to do public schooling (which they all chose to do, to some extent). No math. Math teaching sucks. We kept the math teaching at home.

Yes. The math teaching in high school here is bad. I wonder if those who are good at math do not become high school teachers?

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2 hours ago, Sunday21 said:

Yes. The math teaching in high school here is bad. I wonder if those who are good at math do not become high school teachers?

Correct; they do not. My father was the rare exception. It is appalling to me how abysmally awful almost all public school teachers are at mathematics and real scientific understanding. There are exceptions, but in my experience such exceptions are rare indeed.

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On 9/24/2018 at 9:48 PM, Sunday21 said:

Yes. The math teaching in high school here is bad. I wonder if those who are good at math do not become high school teachers?

 

On 9/25/2018 at 12:22 AM, Vort said:

Correct; they do not. My father was the rare exception. It is appalling to me how abysmally awful almost all public school teachers are at mathematics and real scientific understanding. There are exceptions, but in my experience such exceptions are rare indeed.

My dad is a math genius.  Almost savant-like.  I love that guy but he can't teach math worth a crap.  I got good math skills but I'm a terrible math teacher too - I get easily frustrated when my kid doesn't "see it".  Luckily, my eldest gets it quickly.  My youngest doesn't get it.  I can't teach him - his brains just doesn't work the same way mine and my other kid do.

When I researched middle schools for my kids, I talked to the math teachers.  The arts school had a mediocre math teacher but she wasn't too bad.  But since this was for my eldest kid, I put priority on the "arts" of the art school and supplemented math instruction at home.  The science and technology school math teachers were great!  My youngest did super well there but I still supplemented specialized instruction at home designed for my specific child's brain processes to fill a few gaps.  They're both in high school now and I don't do anything with their school anymore.  They're completely on their own.  I felt they are sufficiently skilled in How To Think.  I believe this is where education in the US is mostly lacking (public or private) - they concentrate more on teaching a kid What to Think rather than How to Think.

My favoritest math teacher when I was in school was that guy who taught us how to extract square root without the help of calculators, then on the term test asked us to extract a cube root.  If you simply learned What to Do in extracting square roots instead of learning How to Do... you're gonna fail his class.

Edited by anatess2
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