Post History
#6: Post edited
by
Canina
·
2021-11-29T23:29:25Z (almost 3 years ago)
Intuitively, why can $a, b$ cycle in ${\color{red}{b}} = \frac c{\color{red}{a}} \iff {\color{red}{a}} = \frac c{\color{red}{b}}$?
I'm NOT asking about algebra behind $ab = c \iff {\color{red}{b}} = \frac c{\color{red}{a}} \iff {\color{red}{a}} = \frac c{\color{red}{b}}.$ 1. Rather, **what's the intuition** why $\color{red}{a, b}$ can swap places, whilst c remains in the numerator?2. **What's this phenomenon or behavior termed**? My son's teacher thinks this is called a _cyclic permutation_, but I want to double check because his teacher admitted he almost failed Abstract Algebra in his [BSc Mathematics Education](https://www.bu.edu/academics/wheelock/programs/mathematics-education/bs/).
- I'm NOT asking about algebra behind $ab = c \iff {\color{red}{b}} = \frac c{\color{red}{a}} \iff {\color{red}{a}} = \frac c{\color{red}{b}}.$
- 1. Rather, what's the intuition why $\color{red}{a, b}$ can swap places, whilst c remains in the numerator?
- 2. What's this phenomenon or behavior called? A cyclic permutation?
#5: Post edited
by
Chgg Clou
·
2021-11-29T17:46:57Z (almost 3 years ago)
I'm NOT asking about algebra behind $ab = c \iff {\color{red}{b}} = \frac c{\color{red}{a}} \iff {\color{red}{a}} = \frac c{\color{red}{b}}.$ 1. Rather, what's the intuition why $\color{red}{a, b}$ can swap places, whilst c remains in the numerator?2. What's this phenomenon or behavior called? A cyclic permutation?
- I'm NOT asking about algebra behind $ab = c \iff {\color{red}{b}} = \frac c{\color{red}{a}} \iff {\color{red}{a}} = \frac c{\color{red}{b}}.$ 1. Rather, **what's the intuition** why $\color{red}{a, b}$ can swap places, whilst c remains in the numerator?
- 2. **What's this phenomenon or behavior termed**? My son's teacher thinks this is called a _cyclic permutation_, but I want to double check because his teacher admitted he almost failed Abstract Algebra in his [BSc Mathematics Education](https://www.bu.edu/academics/wheelock/programs/mathematics-education/bs/).
#4: Post edited
by
Chgg Clou
·
2021-11-29T17:42:33Z (almost 3 years ago)
I'm NOT asking about algebra behind $ab = c \iff {\color{red}{b}} = \frac c{\color{red}{a}} \iff {\color{red}{a}} = \frac c{\color{red}{b}}.$ Rather, what's the intuition why $\color{red}{a, b}$ can swap places, whilst c remains in the numerator? What's this phenomenon or behavior called? A cyclic permutation?
- I'm NOT asking about algebra behind $ab = c \iff {\color{red}{b}} = \frac c{\color{red}{a}} \iff {\color{red}{a}} = \frac c{\color{red}{b}}.$ 1. Rather, what's the intuition why $\color{red}{a, b}$ can swap places, whilst c remains in the numerator?
- 2. What's this phenomenon or behavior called? A cyclic permutation?
#3: Post edited
by
Chgg Clou
·
2021-11-29T17:42:21Z (almost 3 years ago)
I'm NOT asking about algebra behind $ab = c \iff {\color{red}{b}} = \frac c{\color{red}{a}} \iff {\color{red}{a}} = \frac c{\color{red}{b}}.$ Rather, what's the intuition why $\color{red}{a, b}$ can swap places, whilst c remains in the numerator? What's this called?
- I'm NOT asking about algebra behind $ab = c \iff {\color{red}{b}} = \frac c{\color{red}{a}} \iff {\color{red}{a}} = \frac c{\color{red}{b}}.$ Rather, what's the intuition why $\color{red}{a, b}$ can swap places, whilst c remains in the numerator? What's this phenomenon or behavior called? A cyclic permutation?
#2: Post edited
by
Chgg Clou
·
2021-11-29T17:40:24Z (almost 3 years ago)
Intuitively, why can $a, b$ cycle in $\frac c{\color{red}{a}} \iff {\color{red}{a}} = \frac c{\color{red}{b}}$?
- Intuitively, why can $a, b$ cycle in ${\color{red}{b}} = \frac c{\color{red}{a}} \iff {\color{red}{a}} = \frac c{\color{red}{b}}$?
#1: Initial revision
by
Chgg Clou
·
2021-11-29T17:39:29Z (almost 3 years ago)
Intuitively, why can $a, b$ cycle in $\frac c{\color{red}{a}} \iff {\color{red}{a}} = \frac c{\color{red}{b}}$?
I'm NOT asking about algebra behind $ab = c \iff {\color{red}{b}} = \frac c{\color{red}{a}} \iff {\color{red}{a}} = \frac c{\color{red}{b}}.$ Rather, what's the intuition why $\color{red}{a, b}$ can swap places, whilst c remains in the numerator? What's this called?