If you take the number 7 out of the real number line, then

[student34]

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]

Your question is too vague. Explain what you really have in mind.

 

[Mark44]

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.

 

[HallsofIvy]

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]

Your question is too vague. Explain what you really have in mind.

If I take out the number 7, then it seems as though I have something very small but perhaps larger than an infinitesimal like 5/n→∞. Because, we know that 5/n→∞ = 0, but 7 = 7, not 0.

 

[student34]

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.

The "infinitesimal" that I was thinking of is something like 3/n→∞.

 

[Office_Shredder]

3/n→∞.

What you've written doesn't make any sense. Did you mean something like
$$\lim_{n\to \infty} \frac{3}{n} = 0$$?

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]

What you've written doesn't make any sense. Did you mean something like
$$\lim_{n\to \infty} \frac{3}{n} = 0$$?

Yes, I just don't know how to use the proper notation on this forum.

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

Doesn't [7,7] and 7 have similar properties?

 

[Office_Shredder]

Doesn't [7,7] and 7 have similar properties?

Does $$\mathbb{R}$$ and $$\{ \mathbb{R} \}$$ have similar properties? The first being the set of real numbers, and the second being a set which contains a single element, namely the set of real numbers. The answer is no, not in general. Another good example is ∅, the empty set, and {∅}, the set containing only the empty set (in particular it is not empty!)

Any claims that [7,7] (which is the set containing only the number 7, i.e. {7} as has been mentioned above) and 7 the number share similar properties should be clarified in detail: what properties might these share?