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#51 Re: Help Me ! » Quantity, Magnitude, Unit » 2013-08-16 07:29:24
Say x=10 metres: is the magnitude of x 10 or 10 metres? I believe the latter is true.
#52 Help Me ! » Quantity, Magnitude, Unit » 2013-08-16 06:59:46
- atran
- Replies: 5
Hi,
There are at least two types of quantity: scalar quantity and vector quantity. Both have magnitude, but only the vector quantity has direction. A unit is a magnitude. Thus, if F is a vector quantity, then |F| is the magnitude of the quantity.
Am I thinking right?
Thanks for help...
#53 Help Me ! » Inequality Question » 2013-08-05 07:40:23
- atran
- Replies: 1
Hi;
Why: if x1≤y1, x2≤y2, ..., xn≤yn THEN x1+x2+...+xn≤y1+y2+...+yn
Thanks...
#54 Re: Help Me ! » Arithmetic and Significant Digits » 2013-08-05 07:34:52
Of course, you'll still have to justify -1 x -1 = + 1
Is it right to think this way: Think of - as a unary operator and then,
(-a)b= a(-b)=-(ab) => -1*-1 = -(-(1*1)) = 1
(-a)b= a(-b)=-(ab) and -a = (-1)*a => -3*-5 = -(-(3*5)) = 15
Is there a book or a source which clarifies and explains this?
#55 Re: Help Me ! » Arithmetic and Significant Digits » 2013-08-04 07:37:58
I'm thinking like this:
If (a+b)+-(a+b)=0 then, a+b+-(a+b)=0
a+(b + -(a+b))=0 => b + -(a+b) = -a, therefore -(a+b)=-a+-b
#56 Re: Help Me ! » Arithmetic and Significant Digits » 2013-08-03 06:16:20
What about Hardy's A Course of Pure Mathematics (gutenberg.org/ebooks/38769)?
I couldn't find a book which derives the rules by a set of axioms.
Now really, is the minus sign as a prefix a unary operator or is it equivalent to (-1)?
If it's a unary operator, then what is the explanation for [-(a+b)=-a+-b]?
#57 Re: Help Me ! » Arithmetic and Significant Digits » 2013-08-03 00:32:14
I'm really feeling lost... Is there a book you can recommend which explains (with proofs) the rules behind arithmetic and algebra? Should I search for real analysis, abstract algebra, or number theory books?
I've found this book (amazon.com/books/dp/082182693X), but its level seems to be above mine.
#58 Re: Help Me ! » Arithmetic and Significant Digits » 2013-08-02 07:36:27
Say -(a+b): Is the minus sign a unary operator or is the expression equivalent to -1*(a+b)?
#59 Re: Help Me ! » Arithmetic and Significant Digits » 2013-08-02 05:06:27
I don't see how a-(-b) is related to the second rule. First I have to turn it into an addition problem, and since subtracting a number is the same as adding its additive inverse then: a-(-b) = a+b
#60 Re: Help Me ! » Arithmetic and Significant Digits » 2013-08-02 03:35:20
Do you mean a-(-b)?
#61 Re: Help Me ! » Arithmetic and Significant Digits » 2013-08-02 03:00:47
Hi,
Why do so many books and web-pages use these two rules for addition:
1. To add two numbers with the same sign, you add their absolute values and attach their common sign to the sum.
2. To add two numbers with unlike signs, you find the difference between their two absolute values and attach the sign of the number with the larger absolute value to the difference.
Isn't it easier and better to think this way: Say (a) and (b) are two positive real numbers and a>b, then,
a+b is just simple addition
-a+-b = -(a+b), simpler to think this way
a-b is a positive number
b-a = -(a-b), in other words the opposite of the difference
#62 Re: Help Me ! » Number Properties » 2013-08-02 02:05:02
38 = 2*19 => a multiple of a positive odd integer and a positive prime
18 = 2*9 => a multiple of a positive odd integer and a positive prime
8 = 2*4 = 2³ => NOT
#63 Re: Help Me ! » trig » 2013-07-31 07:22:05
tan(54⁰) = height / 300
#64 Help Me ! » What's the formal definition of division? » 2013-07-29 07:24:50
- atran
- Replies: 1
Hi;
I read somewhere that division can be defined as multiplying the dividend by the multiplicative inverse of the divisor: a/b = a * 1/b, but the multiplicative inverse is another division problem.
In the forum (/viewtopic.php?id=19823), I was told that partitive division could be re-written as measurement division. How is that done? I want to know why is division the inverse operation of multiplication. Is there a more formal definition?
Thanks for help.
#65 Re: Maths Is Fun - Suggestions and Comments » Division Pages » 2013-07-28 19:57:22
Hi Bob;
Conceptually, division describes two distinct but related settings. Partitioning involves taking a set of size a and forming b groups that are equal in size. The size of each group formed, c, is the quotient of a and b. Quotative division involves taking a set of size a and forming groups of size c. The number of groups of this size that can be formed, b, is the quotient of a and c.
If the number in each group is known, and you are trying to find the number of groups, then the problem is referred to as a quotative division problem. Quotative division may also be called measurement, or repeated subtraction. You are, in effect, counting or measuring the number of times you can subtract the divisor from the dividend.
If the number of groups is known, and you are trying to find the number in each group, then the problem is referred to as a partitive division problem. Partitive division may also be called equal groups, or sharing and distribution. You are, in effect, partitioning the dividend into the number of groups indicated by the divisor and then counting the number of items in each of the groups.
#66 Maths Is Fun - Suggestions and Comments » Division Pages » 2013-07-28 07:11:11
- atran
- Replies: 5
Hi,
I've read two pages on division, but none includes measurement division. It'll be nice if the author explains and mentions the two types of division.
Thanks...
#67 Re: Help Me ! » Quotient, Ratio, Fraction; What's the difference? » 2013-07-28 06:05:50
Now I got it, thanks...
#68 Re: Help Me ! » Quotient, Ratio, Fraction; What's the difference? » 2013-07-28 03:25:14
I'm thinking like this: If the area of the cake is 1, then it's obvious that one third of the cake is (1/3), therefore two thirds is (2/3).
But it's a bit vague to me, why do the denominator and the numerator represent the whole and the part respectively? I mean, arithmetically, (2/3) means three divides two. From where does the part-to-whole interpretation of division comes from?
#69 Re: Help Me ! » Quotient, Ratio, Fraction; What's the difference? » 2013-07-28 03:11:57
Thanks for the links.
Say I want two thirds of a cake with the area, A. The expression for the wanted area becomes, 2A/3.
As for fractions, I don't understand why the denominator represents the whole and the numerator represents the part.
#70 Help Me ! » Quotient, Ratio, Fraction; What's the difference? » 2013-07-27 07:09:53
- atran
- Replies: 7
Hi,
Am I thinking right? Quotient is the result of division. Ratio relates one quantity to another. Fraction is ratio of two quantities of the same type.
Thanks...
#71 Re: This is Cool » Science Books » 2013-07-24 03:36:02
I spent time searching. However, there are two google features worth knowing:
1) Say you want to search only for pdf files, write the keywords and add filetype:pdf. For example google: c++ quick reference filetype:pdf
2) You can specify what domain you want to search in, for example: square root site:mathsisfun.com
Or say you want to search only in .edu sites, then write: my_keyword site:.edu
#72 Re: This is Cool » Science Books » 2013-07-23 07:35:16
I couldn't post links, that's why I left out the "http" part.
theassayer.org/cgi-bin/asbrowsesubject.cgi?class=Q
freescience.info/books.php?id=4&PHPSESSID=c3046af36f33033bc738fa34f64005betrillia.com/online-math/index.html
cnx.org/content/expanded_browse_subject?subject=Mathematics%20and%20Statistics
people.math.gatech.edu/~cain/textbooks/onlinebooks.html
e-booksdirectory.com/mathematics.php
freemathbooks.com/[/url]
#73 Re: Help Me ! » Why is the square root of (x+y)^2 not (-x-y)? » 2013-07-18 04:54:36
I still don't get it. I learned that √(x) or x^(1/2) is the principal square root of x.
How to think when getting from this step [(x+3)^2 = 13] to [(x+3) = ±√13]?
I mean, why the last step is written like that? Why not (±(x+3)=√13)?
What makes both (±(x+3)=±√13) and (∓(x+3)=±√13) valid?
#74 Re: Help Me ! » Why is the square root of (x+y)^2 not (-x-y)? » 2013-07-16 09:17:12
So there are four ways of expressing it?
1) x+3=√13 => x=√(13)-3
2) -(x+3)=-√13 => x=√(13)-3
3) x+3=-13 => x=-√(13)-3
4) -(x+3)=√13 => x=-√(13)-3
#75 Help Me ! » Why is the square root of (x+y)^2 not (-x-y)? » 2013-07-16 08:56:38
- atran
- Replies: 6
Hi again, this question may seem silly, but I'm confused.
Say, (x^2)+6x-4=0, then by completing the square I get:
(x^2)+6x-4= 0
(x^2)+6x = 4
(x^2)+6x+9= 4+9
(x+3)^2= 13
Now, why isn't sqrt((x+3)^2) also equal to -(x+3)=-x-3?
Many small questions have been popping up in my head. This is leading me to a confused state. I used to do well and understand algebra, but I don't what happened, things started becoming confusing and unclear.