How to Formally Describe Various Sets in Mathematics?

[spaghetti3451]

Homework Statement

Write formal descriptions of the following sets.

(a) The set containing the numbers 1, 10, and 100
(b) The set containing all integers that are greater than 5
(c) The set containing all natural numbers that are less than 5
(d) The set containing the string aba
(e) The set containing the empty string
(f) The set containing nothing at all

Homework Equations

The Attempt at a Solution

(a) $\{1, 10, 100 \}$
(b) $\{ i\ |\ i \in \mathbb{N}\ \text{and}\ i \geq 5 \}$
(c) $\{ 1, 2, 3, 4 \}$
(d) $\{ aba \}$
(e) $\{ \epsilon \}$
(f) $\{ \}$

Are my answers correct?

 

[Svein]

..except that I would have written:
(d) {"aba"}
(e) {""}
(f) Ø

 

[spaghetti3451]

Ah! I see!

I am fairly confident that $\{ \}$ and $\emptyset$ mean the same thing.

Since I am new to the representation of strings, I haven't seen the apostrophe's used for strings before, though!

 

[Mark44]

Homework Statement

Write formal descriptions of the following sets.

(a) The set containing the numbers 1, 10, and 100
(b) The set containing all integers that are greater than 5
(c) The set containing all natural numbers that are less than 5
(d) The set containing the string aba
(e) The set containing the empty string
(f) The set containing nothing at all

Homework Equations

The Attempt at a Solution

(a) $\{1, 10, 100 \}$
(b) $\{ i\ |\ i \in \mathbb{N}\ \text{and}\ i \geq 5 \}$
(c) $\{ 1, 2, 3, 4 \}$
(d) $\{ aba \}$
(e) $\{ \epsilon \}$
(f) $\{ \}$

Are my answers correct?

To add to what Svein said, the answer to (b) should be (b) $\{ i\ |\ i \in \mathbb{N}\ \text{and}\ i > 5 \}$
Do you see the difference?

 

[spaghetti3451]

Yes.