included or not included? lost oversight

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bladeren

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Feb 12, 2023
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Hello,

Again, i lost oversight in the dummy workboek algebra I. What makes a number included? It has to do with the distance from zero? And then to the right? -3 and 5; both not included, because 5 is 2 steps to fur. Uhm, if (-3, 5) was -3,3, then is was included? True or not? It has to do with the interval.

Anyway, what is a good book to learn algebra, where you dont lost oversight? Because, the dummy workbooks, it aint for me... :( sadly enough
 
bladeren said:
Hello,

Again, i lost oversight in the dummy workboek algebra I. What makes a number included? It has to do with the distance from zero? And then to the right? -3 and 5; both not included, because 5 is 2 steps to fur. Uhm, if (-3, 5) was -3,3, then is was included? True or not? It has to do with the interval.

Anyway, what is a good book to learn algebra, where you dont lost oversight? Because, the dummy workbooks, it aint for me... :( sadly enough
Click to expand...
Please show the problem you are solving, and perhaps an image of what your book says, if that is the source of what you are saying. We need to understand your context.

Also, I presume you are not a native English speaker; what do you mean by "oversight"?
 
Note: Original poster's IP address corresponds to the Netherlands.

Eliz.
 
Hello,

thanks for the reply. My english is very bad, there is no dutch forum about algebra. In the dummy's workbook algebra I, i found problem: [-00, 5), (-13, 8], (3, 8), etc... Now, i dont understand when a number is included or not included. When a number is included, you place it in [ ], when it is not included you place it in ( ). They talk about the number line, end numbers, infinite symbol, and how far a number is from zero.

The dummy's workbook isnt for me. Now im looking for a better book. A workbook, that is very clearly. I lost overView and dont know where to begin, to solve a problem. And thats is very frustrating for me. Sometimes it cost me days to look at the algebra problem again. To prevent that i lost overview, i need a book with a short summary from definitions and how to solve al algebra (pre, I, II) problems... Do someone know a good book for me?
 
bladeren said:
Hello,

thanks for the reply. My english is very bad, there is no dutch forum about algebra. In the dummy's workbook algebra I, i found problem: [-00, 5), (-13, 8], (3, 8), etc... Now, i dont understand when a number is included or not included. When a number is included, you place it in [ ], when it is not included you place it in ( ). They talk about the number line, end numbers, infinite symbol, and how far a number is from zero.

The dummy's workbook isnt for me. Now im looking for a better book. A workbook, that is very clearly. I lost overView and dont know where to begin, to solve a problem. And thats is very frustrating for me. Sometimes it cost me days to look at the algebra problem again. To prevent that i lost overview, i need a book with a short summary from definitions and how to solve al algebra (pre, I, II) problems... Do someone know a good book for me?
Click to expand...
You may find this a good place to start (both this particular page, and the site as a whole):


Are you trying to learn from books in English, or have you looked for good books (or sites) in Dutch?
 
[math] x \in [a,\ b] \iff a \le x \le b;\\ x \in (a,\ b] \iff a < x \le b;\\ x \in [a,\ b) \iff a \le x < b; \& \\ x \in (a,\ b) \iff a < x < b. [/math]
Math notation is an international language.
 
Dr.Peterson said:
You may find this a good place to start (both this particular page, and the site as a whole):


Are you trying to learn from books in English, or have you looked for good books (or sites) in Dutch?
Click to expand...
In english.

Aha, i see the problem here: 2<3, 3 is a real number. It can ben 3.848834 and thats why it is ) and not [.
 
JeffM said:
[math] x \in [a,\ b] \iff a \le x \le b;\\ x \in (a,\ b] \iff a < x \le b;\\ x \in [a,\ b) \iff a \le x < b; \& \\ x \in (a,\ b) \iff a < x < b. [/math]
Math notation is an international language.
Click to expand...
Not quite as much as you'd think.

A few years ago I had a student from France, who used a version of interval notation that I was fortunately familiar with from my online interactions; I let her know that I wouldn't force her to use our notation, since she was just here for a year. Here is what she would say:
[math] x \in [a;\ b] \iff a \le x \le b;\\ x \in ]a;\ b] \iff a < x \le b;\\ x \in [a;\ b[ \iff a \le x < b; \& \\ x \in ]a;\ b[ \iff a < x < b. [/math]
Clearly, the semicolon is needed when you use a comma as a decimal separator; and although I like the parenthesis for the open end (which to me suggests that the interval just comes up to that point and barely touches it), I can also see the idea behind the reverse bracket, and perhaps it lets the parentheses be reserved for ordered pairs.

See here:

Interval (mathematics) - Wikipedia

en.wikipedia.org en.wikipedia.org
bladeren said:
Aha, i see the problem here: 2<3, 3 is a real number. It can ben 3.848834 and thats why it is ) and not [.
Click to expand...
It would help us if you would tell us the problem you are referring to, rather than leave us to guess.
 
JeffM said:
[math] x \in [a,\ b] \iff a \le x \le b;\\ x \in (a,\ b] \iff a < x \le b;\\ x \in [a,\ b) \iff a \le x < b; \& \\ x \in (a,\ b) \iff a < x < b. [/math]
Math notation is an international language.
Click to expand...
If its not equal to the variable (x), then it is open --> )
 
bladeren said:
If its not equal to the variable (x), then it is open --> )
Click to expand...
I believe what you mean is that if the symbol between x and a number is > or <, so that equality is not allowed, then we use the parentheses indicating an open end of the interval; if the symbol is [imath]\ge[/imath] or [imath]\le[/imath], so that equality is allowed, then we mark the endpoint as closed, using a bracket, "[" or "]".

That is correct.
 
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