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

1. Jun 17, 2013

### 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]?

2. Jun 17, 2013

### mathman

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

3. Jun 17, 2013

### Staff: Mentor

If you remove 7 from the number line, then you get the real numbers with a point removed. A point has zero length.

4. Jun 17, 2013

### HallsofIvy

Staff Emeritus
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.

5. Jun 17, 2013

### student34

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.

6. Jun 17, 2013

### student34

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

7. Jun 17, 2013

### Office_Shredder

Staff Emeritus
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

8. Jun 17, 2013

### student34

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

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

9. Jun 17, 2013

### Office_Shredder

Staff Emeritus
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?