What does it mean? n followed by a number, e.g. "n23"

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JayG

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Dec 12, 2009, 3:11:14 PM12/12/09
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I'm a new user with a dumb question about the incrementing number that
appears on solutions calculated by TI-Nspire CAS calculator pages.
What do these references mean and how do I interpret or use them? They
are imbedded in solutions where the set of solutions is infinite. For
example:

solve(sin(2*x)=-1,x)
answer: x=((4*n48-1)*pi)/4

solve(sin(2*x)=-1,x)
answer: x=((4*n49-1)*pi)/4

solve(sin(2*x)=-1,x)
answer: x=((4*n50-1)*pi)/4

The number increments, with each new execution of solve on these
equations.

Bryson Perry

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Dec 12, 2009, 3:20:58 PM12/12/09
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n50 is a variable when we solve sin(2*x)=-1 the answer is 3pi/4 +- pi*n when
n is an integer
the calculator writes this as x=((4*n50-1)*pi)/4
--------------------------------------------------
From: "JayG" <jay.g...@gmail.com>
Sent: Saturday, December 12, 2009 3:11 PM
To: "tinspire" <tins...@googlegroups.com>
Subject: [tinspire] What does it mean? n followed by a number, e.g. "n23"
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Sean Bird

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Dec 12, 2009, 3:23:00 PM12/12/09
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These can be avoided by limiting the domain with the 'such that' vertical bar.
E.g.
solve(sin(2*x)=-1,x)|0< x <2pi

Nelson Sousa

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Dec 12, 2009, 5:41:21 PM12/12/09
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The Nspire CAS has two types or generic variables: n1, n2, ..., n99
are arbitrary integers and c1, c2,..., c99 are arbitrary real numbers.
The first type appears quite often when you solve, for example,
trigonometric equations, the second type appears when solving
undetermined systems of equations or differential equations.

They're incremental so that when more than one arbitrary constant is
needed on the same calculation you can tell them apart.

As far as I know you can't reset the count. It will return to n1 or c1
once you reach n99 or c99 resp.


Nelson

JayG

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Dec 13, 2009, 1:31:21 AM12/13/09
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Thanks Bryson. But I still don't understand. I know what value the n-
variable represents in the simple example I used, but how would I
determine it's value if the example were not simple? Or if all the n-
numbers mean the same thing and refer to any integer, then what's the
point of numbering them. If they're all the same, then who cares if
you can tel them apart? When I use the "var" key, I don't see any
reference to these variables. I've only had this calculator for a
couple of weeks. I suspect something really simple is going on here
that I haven't figured out yet.

On Dec 12, 3:20 pm, "Bryson Perry" <brysonperr...@msn.com> wrote:
> n50 is a variable when we solve sin(2*x)=-1 the answer is 3pi/4 +- pi*n when
> n is an integer
> the calculator writes this as x=((4*n50-1)*pi)/4
> --------------------------------------------------
> From: "JayG" <jay.gour...@gmail.com>
> Sent: Saturday, December 12, 2009 3:11 PM
> To: "tinspire" <tins...@googlegroups.com>
> Subject: [tinspire] What does it mean? n followed by a number, e.g. "n23"
>
>
>
> > I'm a new user with a dumb question about the incrementing number that
> > appears on solutions calculated by TI-Nspire CAS calculator pages.
> > What do these references mean and how do I interpret or use them? They
> > are imbedded in solutions where the set of solutions is infinite. For
> > example:
>
> > solve(sin(2*x)=-1,x)
> > answer: x=((4*n48-1)*pi)/4
>
> > solve(sin(2*x)=-1,x)
> > answer: x=((4*n49-1)*pi)/4
>
> > solve(sin(2*x)=-1,x)
> > answer: x=((4*n50-1)*pi)/4
>
> > The number increments, with each new execution of solve on these
> > equations.
>
> > --
> > To post to this group, send email to tins...@googlegroups.com
> > To unsubscribe send email to tinspire+u...@googlegroups.com
> > For more options, visit this group at
> >http://groups.google.com.au/group/tinspire?hl=en-GB?hl=en-GB
> > The tns documents shared by group members are archived at
> >http://lafacroft.com/archive/nspire.php- Hide quoted text -
>
> - Show quoted text -

Nelson Sousa

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Dec 13, 2009, 6:57:53 AM12/13/09
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solve (sin(X)*cos(x) = 0 , x)
the answer is
x= n1 * Pi or x= Pi/2 + n2* Pi
There are two arbitrary constants in the same result, so they muse be numbered.

Now suppose you get two different answers with arbitrary numbers, n1
and n2; if they're not distinct you couldn't use both of them in a
subsequent.

Example:
solve(sin(x)=0,x) returns n1*Pi; solve(sin(3x = 0,x) returns x= n2*Pi/3.
Using copy and paste you can simply type in
solve(x= n1*Pi and x=n2*Pi/3 , n2)
and you get n2 = 3n1, and you determine one of the constants of your
problem from the other.

If the variables weren't numbered you'd have to edit by hand one of
the expressions to change the name of the variable.

Cheers,
Nelson

JayG

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Dec 13, 2009, 2:26:59 PM12/13/09
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Thanks, Nelson. But there's still a piece missing for me.

I think all of our examples use n-something to mean "any integer and
nothing but an integer" in the same sense that pi, e, and i all have
specific meanings that don't change. But it doesn't seem plausible
that the calculator would attach trailing digits that are meaningless
both to the user and to itself.

--Jay
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Nelson Sousa

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Dec 13, 2009, 3:20:33 PM12/13/09
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they're not meaningless if you plan on using the results on a
subsequent calculation or if they come from different degrees of
freedom of the equation(s) you're solving.

Pi, i, e have one and just one value. It doesn't matter how often they
appear in the results, they always mean the same number.

n1, n2, ... are arbitrary integers, they're not constant. And if n1
and n2 come from different equations shouldn't they be labeled
differently? They are completely unrelated, they're not the same
number.

When I solve on paper and need to add an arbitrary integer or constant
I usually use k for integers and t for real parameters. But if I have
more than one of those... I label them k1, k2, ... and t1, t2,... etc.

Nelson

JayG

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Dec 15, 2009, 8:06:07 PM12/15/09
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Hi Nelson--

That's answers the first conditional in my question. You say N23 and
N47 might represent different values or sequences. I didn't know that
because every instance I've seen N-anything always represented "any
integer." So in the examples I've seen so far, it wouldn't matter
what the number was after it.

But if N87 and N15 might stand for something different from "any
integer" and might also be different from each other, then surely the
calculator has a way for the user to ascertain what each means. I
don't see anything when I hit the "Var" key. I also don't see anything
in the documentation about how to find the value of an N-number. So
where does one go inside the the calculator to find the precise
meaning of a particular N number?

As I said, I'm relly new to this.

Jay
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Eric Findlay

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Dec 15, 2009, 9:56:55 PM12/15/09
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Jay, the N numbers are not really variables on the calculator, they're
place-holders in a formula the number following the N is an index, like
a subscript, which the Nspire can't print properly.

--
For I am convinced that neither death nor life, neither angels nor
demons, neither the present nor the future, nor any powers, neither
height nor depth, nor anything else in all creation, will be able to
separate us from the love of God that is in Christ Jesus our Lord.
- Romans 8:38-39 (NIV)
--
Eric Findlay
AKA Eagle-Man
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Nelson Sousa

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Dec 16, 2009, 5:08:04 AM12/16/09
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Those variables don't have specific values. They're arbitrary
integers. They don't have a value, they can have any value as long as
it's integer.

mathematically speaking, if you get

cos(n1*Pi) this is equivalente to cos(k*Pi), forall k in Z.

Cheers,
Nelson

JayG

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Dec 16, 2009, 11:40:21 PM12/16/09
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Thanks everyone. I'm still not certain what the n-numbers mean, but I
have a theory. The theory is derived from some posts and contradicts
others. Please tell me if you think this is wrong.

ITentatively think it is Tinspire's way of naming a closed variable
that has to be a particular subset of integers.

It's closed and not open because, unlike x and y, it's value is
independant and fixed.

It's a variable because, unlike pi, it's value, though independant is
not known.

It's "n" because, unlike other closed variables a, b, and c, it's
fixed value has to be an integer.

It has a number after it because each different n represents a unique
subset of integers, like the n's in the generalized polynomial formula
that represent "the specific integer equal to the number of terms" or
on the cosine example and other trig functions "any integer" (where
the subset is equivalent to the full set.

The specific limitation on the set of possible integers is not
disclosed by Tinspire, because that would have been hard to write the
code for, so TI gave up before it got there during product
development.

Right?

it
it has to be an integer, unlike open variables a and b

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Wayne

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Dec 17, 2009, 10:19:17 AM12/17/09
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Jay,
Your interpretation is definitely incorrect. Let me try to explain
the concept of an arbitrary integer by way of an example.

There are infinitely many solutions to the equation sin(x)=0. Each
multiple of pi is a solution. Without the calculator, we would write
all these infinitely many solutions using the single closed form n*pi
where n can be any one of the integers 0, plus or minus 1, plus or
minus 2, plus or minus 3,....... The ellipsis indicate that the list
is infinite. When the Nspire solves this or any problem in which
there can be infinitely many solutions, the calculator simply writes
the single closed form n*pi to indicate that any one of the integers
can be substituted for n in order to obtain a particular solution.
The calculator needs to distinguish the arbitrary constants from one
another for several reasons. The most important in my mind occurs
when a solution needs two or more such constants to completely specify
the solution. The best example I can think of for this case is the
solution of differential equations. For example, a fourth order
differential equation requires three arbitrary constants to completely
specify all the solutions. The Nspire CAS solution would include c1
and c2 and c3 as arbitrary constants in the solution. Of course the
increments would vary in each calculator depending on how many had
been used in the solutions of previous equations in the same problem
in the .tns document. Try this for yourself using the very nice
linear algebra and differential equation library that is now included
with the OS. Hope this helps clear your confusion.
Wayne

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Wayne

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Dec 17, 2009, 10:24:19 AM12/17/09
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I had a typo in this post. I meant to say third order differential
equations requires three constants to completely specify all
solutions. Sorry for the mistake; I should proofread my submissions
more carefully.
Wayne

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