2 - 5⁄2 = 3 - 5⁄2
therefore 2 = 3
is explained thus:—The fallacy lies in ignoring the fact that the square roots are plus or minus. In the working we have taken both roots as plus. If we take one root plus, and the other minus, and add 5⁄2, we have either 2 = 2, or 3 = 3.
20.
The largest possible parcel which can be sent through the post under the official limits of 3 feet 6 inches in length, and 6 feet in length and girth combined, is a cylinder 2 feet long and 4 feet in circumference, the cubic contents of which are 26⁄11 cubic feet.
21.
We can show, or seem to show, that either four, five, or six nines amount to 100, thus:—
| 999⁄9 = 100 | IX IX IX IX IX 100 | 9 × 9 + 9 + 99⁄9 = 100 |