Post History
#6: Post edited
by
Anixx
·
2026-05-08T11:14:47Z (4 months ago)
First, maybe this is not what you want to hear, but wheel theory is not necessary to naturally define $0/0$. If you define $0/0=0$, you will have all the main algebraic rules kept (including associativity and distributivity), plus will get other benefits, for instance, embedding of the trivial ring into reals. It is also supported by pseudo-inverse matrices, which allow to define division by zero divisors among other things.- And you really do not need the multiplicative inverse of zero for this as you can define division separately.
- It is also compatible with the projective real line, where division by zero is defined, if you also postulate $0\cdot\infty=0$, which is also convenient.
- Second, the cardinal numbers are usually equated with a subset of surreals, but with different arithmetic rules. As such, $\aleph_0$ is usually equalized with $\omega$, and using surreal division, $\omega/\omega=1$. This is also true for any other non-zero surreal number.
- First, maybe this is not what you want to hear, but wheel theory is not necessary to naturally define $0/0$. If you define $0/0=0$, you will have all the main algebraic rules kept (including associativity and distributivity), plus will get other benefits, for instance, embedding of the trivial ring into reals. It is also supported by pseudo-inverse matrices, which allow to define division of zero divisors by other zero divisors among other things.
- And you really do not need the multiplicative inverse of zero for this as you can define division separately.
- It is also compatible with the projective real line, where division by zero is defined, if you also postulate $0\cdot\infty=0$, which is also convenient.
- Second, the cardinal numbers are usually equated with a subset of surreals, but with different arithmetic rules. As such, $\aleph_0$ is usually equalized with $\omega$, and using surreal division, $\omega/\omega=1$. This is also true for any other non-zero surreal number.
#5: Post edited
by
Anixx
·
2026-05-08T01:49:29Z (4 months ago)
- First, maybe this is not what you want to hear, but wheel theory is not necessary to naturally define $0/0$. If you define $0/0=0$, you will have all the main algebraic rules kept (including associativity and distributivity), plus will get other benefits, for instance, embedding of the trivial ring into reals. It is also supported by pseudo-inverse matrices, which allow to define division by zero divisors among other things.
- And you really do not need the multiplicative inverse of zero for this as you can define division separately.
- Second, the cardinal numbers are usually equated with a subset of surreals, but with different arithmetic rules. As such, $\aleph_0$ is usually equalized with $\omega$, and using surreal division, $\omega/\omega=1$. This is also true for any other non-zero surreal number.
- First, maybe this is not what you want to hear, but wheel theory is not necessary to naturally define $0/0$. If you define $0/0=0$, you will have all the main algebraic rules kept (including associativity and distributivity), plus will get other benefits, for instance, embedding of the trivial ring into reals. It is also supported by pseudo-inverse matrices, which allow to define division by zero divisors among other things.
- And you really do not need the multiplicative inverse of zero for this as you can define division separately.
- It is also compatible with the projective real line, where division by zero is defined, if you also postulate $0\cdot\infty=0$, which is also convenient.
- Second, the cardinal numbers are usually equated with a subset of surreals, but with different arithmetic rules. As such, $\aleph_0$ is usually equalized with $\omega$, and using surreal division, $\omega/\omega=1$. This is also true for any other non-zero surreal number.
#4: Post edited
by
Anixx
·
2026-05-08T01:44:39Z (4 months ago)
First, maybe this is not what you want to hear, but wheel theory is not necessary to naturally define $0/0$. If you define $0/0=0$, you will have all the main algebraic rules kept (including associativity and distributivity), plut will get other benefits, for instance, embedding of the trivial ring into reals. It is also supported by pseudo-inverse matrices, which allow to define division by zero divisors among other things.- And you really do not need the multiplicative inverse of zero for this as you can define division separately.
- Second, the cardinal numbers are usually equated with a subset of surreals, but with different arithmetic rules. As such, $\aleph_0$ is usually equalized with $\omega$, and using surreal division, $\omega/\omega=1$. This is also true for any other non-zero surreal number.
- First, maybe this is not what you want to hear, but wheel theory is not necessary to naturally define $0/0$. If you define $0/0=0$, you will have all the main algebraic rules kept (including associativity and distributivity), plus will get other benefits, for instance, embedding of the trivial ring into reals. It is also supported by pseudo-inverse matrices, which allow to define division by zero divisors among other things.
- And you really do not need the multiplicative inverse of zero for this as you can define division separately.
- Second, the cardinal numbers are usually equated with a subset of surreals, but with different arithmetic rules. As such, $\aleph_0$ is usually equalized with $\omega$, and using surreal division, $\omega/\omega=1$. This is also true for any other non-zero surreal number.
#3: Post edited
by
Anixx
·
2026-05-07T22:51:04Z (4 months ago)
First, maybe this is not what you want to hear, but wheel theory is not necessary to naturally define $0/0$. If you define $0/0=0$, you will have all the main algebraic rules kept (including associativity and distributivity), plut will get other benefits, for instance, embedding of the trivial ring into reals. It is also supported by pseudo-inverse matrices. And you really do not need the multiplicative inverse of zero for this as you can define division separately.- Second, the cardinal numbers are usually equated with a subset of surreals, but with different arithmetic rules. As such, $\aleph_0$ is usually equalized with $\omega$, and using surreal division, $\omega/\omega=1$. This is also true for any other non-zero surreal number.
- First, maybe this is not what you want to hear, but wheel theory is not necessary to naturally define $0/0$. If you define $0/0=0$, you will have all the main algebraic rules kept (including associativity and distributivity), plut will get other benefits, for instance, embedding of the trivial ring into reals. It is also supported by pseudo-inverse matrices, which allow to define division by zero divisors among other things.
- And you really do not need the multiplicative inverse of zero for this as you can define division separately.
- Second, the cardinal numbers are usually equated with a subset of surreals, but with different arithmetic rules. As such, $\aleph_0$ is usually equalized with $\omega$, and using surreal division, $\omega/\omega=1$. This is also true for any other non-zero surreal number.
#2: Post edited
by
Anixx
·
2026-05-07T22:50:04Z (4 months ago)
- First, maybe this is not what you want to hear, but wheel theory is not necessary to naturally define $0/0$. If you define $0/0=0$, you will have all the main algebraic rules kept (including associativity and distributivity), plut will get other benefits, for instance, embedding of the trivial ring into reals. It is also supported by pseudo-inverse matrices. And you really do not need the multiplicative inverse of zero for this as you can define division separately.
Second, the cardinal numbers are usually equated with a subset of surreals, but with different arithmetic rules. As such, $\aleph_0$ is usually equalized with $\omega$, and using surreal division, $\omega/\omega=1$.
- First, maybe this is not what you want to hear, but wheel theory is not necessary to naturally define $0/0$. If you define $0/0=0$, you will have all the main algebraic rules kept (including associativity and distributivity), plut will get other benefits, for instance, embedding of the trivial ring into reals. It is also supported by pseudo-inverse matrices. And you really do not need the multiplicative inverse of zero for this as you can define division separately.
- Second, the cardinal numbers are usually equated with a subset of surreals, but with different arithmetic rules. As such, $\aleph_0$ is usually equalized with $\omega$, and using surreal division, $\omega/\omega=1$. This is also true for any other non-zero surreal number.
#1: Initial revision
by
Anixx
·
2026-05-07T22:33:30Z (4 months ago)
First, maybe this is not what you want to hear, but wheel theory is not necessary to naturally define $0/0$. If you define $0/0=0$, you will have all the main algebraic rules kept (including associativity and distributivity), plut will get other benefits, for instance, embedding of the trivial ring into reals. It is also supported by pseudo-inverse matrices. And you really do not need the multiplicative inverse of zero for this as you can define division separately. Second, the cardinal numbers are usually equated with a subset of surreals, but with different arithmetic rules. As such, $\aleph_0$ is usually equalized with $\omega$, and using surreal division, $\omega/\omega=1$.