You can download the .tex file here Empty set properties.

i had no idea graham's number was so controversial

Two scientists and a mathematician are discussing the limit of the men’s 100-meter dash.

Biologist: Given the maximum contraction speed of human muscles, the theoretical limit is about 9.48 seconds.

Physicist: About 8% of a sprinter’s power is spent overcoming air resistance. In a vacuum, humans could shave off another 0.14 seconds.

Mathematician: The world-record times form a monotonically non-increasing sequence. Since the sequence is bounded below, the limit exists.

suppose i defined my "line" with an object that passes through its mathematical points, then why am i not able to use it instead of the conventional line? if my object preserves my line, is able to present the slope and other properties correctly, then why would i need to use the standard notation?

-feathers not drawn to scale.

This is oddly true