Post History
#2: Post edited
by
Chgg Clou
·
2022-10-09T00:25:15Z (over 1 year ago)
- On one hand, I know that algebraically, $\dfrac{3}1 ≡ \dfrac{1}{\color{red}{1/3}}$.
On the other hand, they differ in practice, not least because $\color{red}{1/3}$ contains 3 as the repetend. For example, if I need a physical scrap of material to have a 3:1 ratio but have a length of 3 m, then I can fulfill this requirement by making the width 1 m.But presuppose a length of 1 m. Then a 3:1 ratio is impossible to accomplish, because a 3:1 ratio would require a width of $\color{red}{1/3=0.\overline{3}}$. But it's impossible to measure and cut anything physical at a repeating decimal!- Doesn't this physical impossibility due to the reptend belie, or undermine, the theoretical "equality" that $\dfrac{3}1 ≡ \dfrac{1}{\color{red}{1/3}}$? How can this physical impossibility due to the repetend be reconciled with equality?
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- On one hand, I know that algebraically, $\dfrac{3}1 ≡ \dfrac{1}{\color{red}{1/3}}$.
- On the other hand, they differ in practice, not least because $\color{red}{1/3}$ contains 3 as the repetend. For example, if a scrap of physical material must have a 3:1 ratio and a length of 3 m, then I shall make the width 1 m.
- But presuppose a length of 1 m. Then a 3:1 ratio is impossible to accomplish, because it would require a width of $\color{red}{1/3=0.\overline{3}}$. But it's impossible to measure and cut anything physical at a repetend!
- Doesn't this physical impossibility due to the reptend belie, or undermine, the theoretical "equality" that $\dfrac{3}1 ≡ \dfrac{1}{\color{red}{1/3}}$? How can this physical impossibility due to the repetend be reconciled with equality?
- 
#1: Initial revision
by
Chgg Clou
·
2022-10-09T00:23:58Z (over 1 year ago)
How can 3/1 ≡ 1/(1/3), when left side features merely integers, but right side features a repetend?
On one hand, I know that algebraically, $\dfrac{3}1 ≡ \dfrac{1}{\color{red}{1/3}}$.
On the other hand, they differ in practice, not least because $\color{red}{1/3}$ contains 3 as the repetend. For example, if I need a physical scrap of material to have a 3:1 ratio but have a length of 3 m, then I can fulfill this requirement by making the width 1 m.
But presuppose a length of 1 m. Then a 3:1 ratio is impossible to accomplish, because a 3:1 ratio would require a width of $\color{red}{1/3=0.\overline{3}}$. But it's impossible to measure and cut anything physical at a repeating decimal!
Doesn't this physical impossibility due to the reptend belie, or undermine, the theoretical "equality" that $\dfrac{3}1 ≡ \dfrac{1}{\color{red}{1/3}}$? How can this physical impossibility due to the repetend be reconciled with equality?
