MHB Visual proof of if ∞=1/0, then 0=1/∞

  • Thread starter Thread starter anemone
  • Start date Start date
  • Tags Tags
    Proof Visual
Click For Summary
The discussion presents a visual proof asserting that if ∞ equals 1/0, then 0 must equal 1/∞. The proof involves rotating the equation counterclockwise by 90 degrees, leading to the equation 8 = -10. After manipulating the equation by subtracting 8, it concludes that 0 equals -18. The proof is then reversed to demonstrate that 0 indeed equals 1/∞. This approach humorously addresses the question of what was divided to reach such conclusions.
anemone
Gold Member
MHB
POTW Director
Messages
3,851
Reaction score
115
A visual proof of the following statement:

If $\infty=\dfrac{1}{0}$, then $0=\dfrac{1}{\infty}$ .

Proof:

Assume $\infty=\dfrac{1}{0}$. Rotate each side of the equation counterclockwise $90^{\circ}$. We get 8 = −10. Subtract 8, getting 0 = −18. Then rotate both parts back: $0=\dfrac{1}{\infty}$. QED.
 
Mathematics news on Phys.org
anemone said:
A visual proof of the following statement:

If $\infty=\dfrac{1}{0}$, then $0=\dfrac{1}{\infty}$ .

Proof:

Assume $\infty=\dfrac{1}{0}$. Rotate each side of the equation counterclockwise $90^{\circ}$. We get 8 = −10. Subtract 8, getting 0 = −18. Then rotate both parts back: $0=\dfrac{1}{\infty}$. QED.
I think this proof answers the question: "What did you divide by this time??"

-Dan
 
I have been insisting to my statistics students that for probabilities, the rule is the number of significant figures is the number of digits past the leading zeros or leading nines. For example to give 4 significant figures for a probability: 0.000001234 and 0.99999991234 are the correct number of decimal places. That way the complementary probability can also be given to the same significant figures ( 0.999998766 and 0.00000008766 respectively). More generally if you have a value that...

Similar threads

  • · Replies 55 ·
2
Replies
55
Views
6K
  • · Replies 2 ·
Replies
2
Views
1K
  • · Replies 3 ·
Replies
3
Views
2K
  • · Replies 6 ·
Replies
6
Views
2K
  • · Replies 7 ·
Replies
7
Views
3K
  • · Replies 1 ·
Replies
1
Views
2K
Replies
6
Views
2K
  • · Replies 6 ·
Replies
6
Views
2K
  • · Replies 20 ·
Replies
20
Views
1K
Replies
17
Views
1K