Reading

Read the following. While reading, observe how convictions emerge, change, or disappear.

Let

$$x = 0.\overline{9}$$

Multiply both sides by $10$.

$$ 10x = 9.\overline{9} $$

Since $9.\overline{9}=9+0.\overline{9}$, we can write:

$$ 10x = 9 + 0.\overline{9} $$

Since $x=0.\overline{9}$, we can substitute $x$:

$$ 10x = 9 + x $$

Subtract $x$ from both sides.

$$ 9x = 9 $$

Divide by $9$.

$$ x = 1 $$

Since $x=0.\overline{9}$ and $x=1$:

$$ 0.\overline{9} = 1 $$

Now read the following. While reading, observe how convictions emerge, change, or disappear.

Like to the falling of a star,
Or as the flights of eagles are,
Or like the fresh spring's gaudy hue,
Or silver drops of morning dew,
Or like a wind that chafes the flood,
Or bubbles which on water stood:
Even such is man, whose borrowed light
Is straight called in, and paid to night.
The wind blows out, the bubble dies;
The spring entombed in autumn lies;
The dew dries up, the star is shot;
The flight is past, and man forgot.

[Sic Vita by Henry King (1592-1669)]