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February 5th, 2013, 07:01 AM   #1
r0i
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Learning to read maths formulas

Hi,
im new in the forum, nice to meet you!
I'm engineer and I want improve my mathematical reading, i.e. formula syntaxis, im very noob in this.

My doubt is:
having:



to iterate through every element of S set, its the same write:



that





Take it easy , and thanks for your time.

--
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r0i.
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February 5th, 2013, 07:19 AM   #2
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Re: Learning to read maths formulas

Yes, they are the same. In the former notation, you can drop the subscript and just write
This is mostly used in cases where the elements are not listed “nicely” like . For example, if is the set of prime numbers less than 100, then the above is a way of expressing the sum of all primes numbers less than 100.
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February 5th, 2013, 07:27 AM   #3
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Re: Learning to read maths formulas

Hi Crimson Sunbird,

thanks for your fast answer, and for the subscript tip.

I understand it, in cases like you described, the abbreviation has "implicit information".
Again thanks for your time.

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r0i.
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February 5th, 2013, 07:35 AM   #4
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Re: Learning to read maths formulas

I don't think of that as an abbreviation. I see as an abbreviation for so this one works out to be



where the latter has the advantage of not needing an explicit numbering of the elements.
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February 5th, 2013, 07:48 AM   #5
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Re: Learning to read maths formulas

Hi CRGreathouse,

in this context, n is the maximum value that can reach the subscript, i.e. indicating max. no. of elements in the set,
and k is the current element, so in that case i think yes, as Crimson Sunbird said.

In your last equation, I understand that you try get every element in S n times, or in python:

Code:
for k in range(n):
    for s in S:
        # stuff
I misunderstood?
Thanks for your time .
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Roi.
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February 5th, 2013, 09:00 AM   #6
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Re: Learning to read maths formulas

Quote:
Originally Posted by r0i
I misunderstood?
Yes. On either side of the equation each term appears only once, not n times. (n elements total, not n^2.) So if S = {1, 2} either side gives you 1 + 2 = 3, not 1 + 1 + 2 + 2 = 6.
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February 5th, 2013, 09:08 AM   #7
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Re: Learning to read maths formulas

ok, then we cant do directly:
Code:
for s in S:
   #stuff
we must iterate over the subscript, and use it as index in S:
Code:
for k in range(n):
    sk = S[k]
    # stuff
Right?
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February 5th, 2013, 09:29 AM   #8
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Re: Learning to read maths formulas

Actually, Im reading in a paper called "A new fuzzing method using multi data samples"
where a a equation in the form I posted is showed.
The information given is the next:


In which:
sk, kth data sample of input elements to a target software
mined, S is a primitive set of the data sample.


And

S? is a set constituted by representative
elements selected from S, and S? is the data sample
combination to be used to generate test cases.

[...]

Tr1 and Tr2 are two different transformers form sk to
sampletreek,, M is a set of mutators,


The next pseudo-code is showed:
Code:
1. M = {m1, …, mi, …, mw }
2. testsuite = {}
3. for (each sk in S?)
4. {
5.    sampletreek = Tr1 (sk)
6.    for (each mi in M except GAMutator)
7.    {
8.       MTS = ... #stuff
15.  }
16. }
17. 
run every element in testsuite in the target
software and monitor them
Then the equation appears:


With this I related the first summation with the for loop on l.3,
and the boundaries of the second with the l.1 M = {m1, …, mi, …, mw }
i, k and the for loop on l.6.

In the practice it seems the same, iteratoins over arrays/lists/sets, as you
can see in pseudo-code :S.

Some help to clarify ?
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February 5th, 2013, 11:11 AM   #9
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Re: Learning to read maths formulas

Quote:
Originally Posted by r0i
Right?
No, just the opposite: usually in post-high-school math you don't use indices, you use elements of a set.
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February 5th, 2013, 11:17 AM   #10
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Re: Learning to read maths formulas

Quote:
Originally Posted by r0i


With this I related the first summation with the for loop on l.3,
and the boundaries of the second with the l.1 M = {m1, …, mi, …, mw }
i, k and the for loop on l.6.

In the practice it seems the same, iteratoins over arrays/lists/sets, as you
can see in pseudo-code :S.

Some help to clarify ?
This could equally be written

and means the sum of the absolute value of m_i(Tr(s)) over all s in S and all i from 1 to w. There are #S * w summands in total, where #S is the number of elements in S.
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