Is Zero Considered a Number in ZF Set Theory?

  • Thread starter Thread starter Erdem
  • Start date Start date
  • Tags Tags
    Zero
Erdem
what is zero in math.
 
Mathematics news on Phys.org
It's an integer. Can you be more specific?

- Warren
 
By ZF set theory this is the cardinal of the empty set.

0 = |{}| (no content exists)
 

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 »

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 'Imaginary Pythagorus'

Thread 'Imaginary Pythagorus'

I posted this in the Lame Math thread, but it's got me thinking. Is there any validity to this? Or is it really just a mathematical trick? Naively, I see that i2 + plus 12 does equal zero2. But does this have a meaning? I know one can treat the imaginary number line as just another axis like the reals, but does that mean this does represent a triangle in the complex plane with a hypotenuse of length zero? Ibix offered a rendering of the diagram using what I assume is matrix* notation...
View full post »

Similar threads

I Can I add any number of zeros to 0.00 ... 1?
Replies
30
Views
2K
Insights Why Division by Zero is a Bad Idea
Replies
47
Views
6K
B Is Infinity Essential in Set Theory's ZF Axioms?
Replies
2
Views
2K
MHB Zero: Natural or Counting Number?
Replies
6
Views
4K
B Does Infinity Times Two Equal Infinity and Other Mathematical Paradoxes?
Replies
7
Views
2K
B Is one out of infinity different from zero?
Replies
31
Views
2K
I What is an object with a zero square?
Replies
6
Views
1K
I Division of a complex number by zero
Replies
7
Views
4K
I Expressing any given point on plane with one unique number
Replies
4
Views
2K
B Imaginary Pythagorus
Replies
10
Views
122

Hot Threads

Recent Insights

Back
Top