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student34
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what can be said about 7? Is it like an infinitesimal? Is it smaller or bigger? What is it? Is it just [7,7]?
If you remove 7 from the number line, then you get the real numbers with a point removed. A point has zero length.student34 said:what can be said about 7? Is it like an infinitesimal? Is it smaller or bigger? What is it? Is it just [7,7]?
mathman said:Your question is too vague. Explain what you really have in mind.
HallsofIvy said:Of the choices given, "[7, 7]", which is exactly the same as the set notation "{7}" is best. It is a single point. You would have to define exactly what you mean by "infinitesimal" in this context before anyone could answer your other questions.
student34 said:3/n→∞.
Office_Shredder said:What you've written doesn't make any sense. Did you mean something like
[tex] \lim_{n\to \infty} \frac{3}{n} = 0 [/tex]?
It's not clear to me why you think this is related to the number 7. The length of the interval [7,7] is completely unrelated to the number 7 itself
student34 said:Doesn't [7,7] and 7 have similar properties?
If you take out 7 from the real number line, it creates a gap or hole in the line. This means that there is now a discontinuity in the number line at that point. The numbers on either side of the gap are still considered real numbers, but the number 7 itself is no longer included in the set of real numbers.
Yes, you can still perform mathematical operations on the numbers on either side of the gap. The gap created by removing 7 does not affect the properties of the real numbers, so basic operations such as addition, subtraction, multiplication, and division can still be performed.
Removing 7 does not affect the order of the numbers on the real number line. The numbers on either side of the gap are still ordered from least to greatest, and the gap itself does not change the relative positions of the numbers.
No, the gap created by removing 7 is not considered a real number. It is simply an empty point on the number line where the number 7 used to be. Real numbers are defined as all rational and irrational numbers, and the gap does not fit this definition.
Removing 7 does not affect the properties of the real numbers. The real numbers still maintain their fundamental properties, such as closure under addition and multiplication, commutativity, associativity, and distributivity. The gap created by removing 7 does not change these properties.