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Muu9
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No of course not, it's just notation, like x "approaching infinity" in the case of some limits.gmax137 said:Yes but my question was, does it make any sense for a closed set to have "infinity" as an upper bound?
No of course not, it's just notation, like x "approaching infinity" in the case of some limits.gmax137 said:Yes but my question was, does it make any sense for a closed set to have "infinity" as an upper bound?
If infinity is one of the limits for an interval, this is not a clearly understood precise number or value, so that end of the interval remains "open"; so this is why the parenth is used to show that side of the interval (the inner curve of the parenth facing the infinity symbol).Muu9 said:No of course not, it's just notation, like x "approaching infinity" in the case of some limits.
sbrothy said:I'm again on thin ice here but from what I've heard from college mathematics introductions some start courses simply assume that pupils didn't understand or pay sufficient attention during high school and thus start from scratch quickly going through the basics just in case.
Your remark is correct. I guess, no matter the context or the notation, including infinity limit requires special attention. Thanks for bringing it up.gmax137 said:Yes but my question was, does it make any sense for a closed set to have "infinity" as an upper bound?
I learned infinity is always written as an open-ended set. Thus [2, ∞] makes no sense. Is the same true with the American notation?gmax137 said:Yes but my question was, does it make any sense for a closed set to have "infinity" as an upper bound?
Yes, in American notation it would be written [2, infinity)sbrothy said:I learned infinity is always written as an open-ended set. Thus [2, ∞] makes no sense. Is the same true with the American notation?
In theory, there's this Compactification of the Reals; one-point or 2-point compactification that includes one of ##\pm \infty ##.gmax137 said:Sorry for the tangent, but ...
What does the ,∞[ part mean? I understand if you write [2,b[ you mean everything from 2 up to but not including b. But when you put the upper limit as ∞, it is unbounded, right?
So I am asking, what's the difference between [2,∞[ and [2,∞] ?
Or [2,∞) and [2,∞]
No, "College Algebra" is not the same as high school "Algebra II." While both courses cover algebraic concepts such as equations, functions, and graphs, "College Algebra" is typically more advanced and covers additional topics such as matrices, logarithms, and complex numbers.
It depends on your academic goals and the requirements of your college or university. Some schools may allow you to place out of "College Algebra" if you received a high enough grade in "Algebra II" or if you pass a placement test. However, if you plan on pursuing a degree in a math-related field, it may be beneficial to take "College Algebra" to build a strong foundation.
Again, this can vary depending on the specific curriculum and instructor. However, in general, "College Algebra" is considered to be more challenging than "Algebra II" due to its more comprehensive coverage of advanced algebraic concepts.
Yes, "College Algebra" is an important prerequisite for many higher level math courses such as calculus, statistics, and linear algebra. It provides the necessary foundation and skills for success in these courses.
It is not recommended to skip "College Algebra" and go straight to Calculus. "College Algebra" covers fundamental algebraic concepts that are essential for success in calculus. Skipping this course may put you at a disadvantage and make it more difficult to understand and apply calculus concepts.