MHB Prove: 2ε{a,2,b} in Set Theory

AI Thread Summary
The discussion centers on proving that 2 is an element of the set {a, 2, b} within axiomatic set theory. Participants seek clarity on the definitions of the set notation "{a, 2, b}" and the membership symbol "ε." The set is defined as the union of {a, 2} and {b}, which can be expressed as {a, 2} ∪ {b}. A reference to a similar problem and its solution is mentioned, but external links are discouraged. The conversation emphasizes the importance of understanding set definitions and notation in axiomatic set theory.
solakis1
Messages
407
Reaction score
0
Prove in any axiomatic set theory that:2ε{a,2,b} , where a,b are letters
 
Mathematics news on Phys.org
What is the definition of "{a, 2, b}" in "axiomatic set theory"? What is the definition of "ε"?
 
Country Boy said:
What is the definition of "{a, 2, b}" in "axiomatic set theory"? What is the definition of "ε"?

{a,2,b}={a,2}U{b}
 
solakis said:
{a,2,b}={a,2}U{b}
Or even better, starting from where you left off: [math]\{ a, 2 \} \cup \{ b \} = \left ( \{ a \} \cup \{ 2 \} \right ) \cup \{ b \}[/math]

-Dan
 
solakis said:
here is the solution for a similar problem given by seppel in MHF

From our guidelines:

Please do not give a link to another site as a means of providing a solution, either by the author of the thread posted here, or by someone responding with a solution.
 

Thread 'Non-orthogonal bases'

Suppose ,instead of the usual x,y coordinate system with an I basis vector along the x -axis and a corresponding j basis vector along the y-axis we instead have a different pair of basis vectors ,call them e and f along their respective axes. I have seen that this is an important subject in maths My question is what physical applications does such a model apply to? I am asking here because I have devoted quite a lot of time in the past to understanding convectors and the dual...
View full post »

Thread 'Fermat's Last Theorem'

Fermat's Last Theorem has long been one of the most famous mathematical problems, and is now one of the most famous theorems. It simply states that the equation $$ a^n+b^n=c^n $$ has no solutions with positive integers if ##n>2.## It was named after Pierre de Fermat (1607-1665). The problem itself stems from the book Arithmetica by Diophantus of Alexandria. It gained popularity because Fermat noted in his copy "Cubum autem in duos cubos, aut quadratoquadratum in duos quadratoquadratos, et...
View full post »

Thread 'What Exactly is Dirac’s Delta Function? - Insight'

Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. In Dirac’s Principles of Quantum Mechanics published in 1930 he introduced a “convenient notation” he referred to as a “delta function” which he treated as a continuum analog to the discrete Kronecker delta. The Kronecker delta is simply the indexed components of the identity operator in matrix algebra Source: https://www.physicsforums.com/insights/what-exactly-is-diracs-delta-function/ by...
View full post »

Similar threads

MHB Is Theorem 5.2 in SET THEORY AND LOGIC True or False?
Replies
2
Views
1K
MHB The Union of Two Open Sets is Open
Replies
3
Views
2K
I Is It Valid to Cancel Sets in Set Theory?
Replies
11
Views
1K
I (0,1) is uncountable using binary expansions?
Replies
15
Views
2K
I On base-b expansion of nonnegative reals
Replies
7
Views
2K
I Questions regarding Kurepa's Conjecture
Replies
1
Views
2K
B Is this the right set mapping notation for a limit in two variables?
Replies
8
Views
1K
MHB Is this Trigonometric Expression a Constant Function of x?
Replies
2
Views
1K
Question about "or" in set theory
Replies
3
Views
2K
I System to represent objects in Mathematics
Replies
38
Views
4K

Hot Threads

Recent Insights

Back
Top