How to Formally Describe Various Sets in Mathematics?

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Discussion Overview

The discussion revolves around the formal descriptions of various mathematical sets, including specific examples such as sets of numbers, strings, and the empty set. Participants are engaged in a homework-related context, providing their attempts at solutions and seeking validation of their answers.

Discussion Character

  • Homework-related, Mathematical reasoning

Main Points Raised

  • One participant presents formal descriptions for several sets, including specific numbers and conditions for integers and natural numbers.
  • Another participant suggests alternative notations for representing strings and the empty set, indicating a preference for different symbols.
  • A participant expresses confidence that two representations of the empty set are equivalent.
  • There is a correction proposed regarding the condition for integers greater than 5, suggesting it should be strictly greater (i > 5) rather than greater than or equal to (i ≥ 5).

Areas of Agreement / Disagreement

Participants generally agree on the formal descriptions provided, but there are differing opinions on the notation for strings and the condition for integers greater than 5, indicating unresolved preferences and interpretations.

Contextual Notes

Some participants express uncertainty about the representation of strings and the use of specific symbols, which may reflect varying levels of familiarity with mathematical notation.

spaghetti3451
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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?
 
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..except that I would have written:
(d) {"aba"}
(e) {""}
(f) Ø
 
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!
 
failexam said:

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?
 
Yes.
 

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