Reading

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

Let x = 0.999...

Multiply both sides by 10.

10x = 9.999...

Split the right-hand side.

10x = 9 + 0.999...

Replace 0.999... by x.

10x = 9 + x

Subtract x from both sides.

9x = 9

Divide by 9.

x = 1

Therefore

0.999... = 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)]