In about half an hour, UK #ISS pass, starting at 21:58:57, duration 54 secs, visible, Magnitude -1.3

In about half an hour, UK #ISS pass, starting at 20:23:08, duration 228 secs, bright, Magnitude -2.5

Some passes of the #ISS visible from the UK overnight - I'll tweet/toot warnings closer to the time

In about half an hour, UK #ISS pass, starting at 21:11:12, duration 120 secs, bright, Magnitude -2.4

Some passes of the #ISS visible from the UK overnight - I'll tweet/toot warnings closer to the time

In about half an hour, UK #ISS pass, starting at 20:24:51, duration 91 secs, visible, Magnitude -1.7

Some passes of the #ISS visible from the UK overnight - I'll tweet/toot warnings closer to the time

It's well known that \( |\mathbb{N}| = |\mathbb{N}^2| \) and it's not hard to make an explicit 1-1 mapping. Ditto \( |\mathbb{Q}| = |\mathbb{Q}^2| \).

We also know that \( |\mathbb{R}| = |\mathbb{R}^2| \).

Your challenge, should you decide to accept it, it to give an explicit one-to-one mapping.

Go ...

@cerisara No problem ... happy to help (when I can!)

@cerisara So in particular:

\( \frac{f(x)}{x²} \)

@cerisara There is, you open with backslash round bra and close with backslash round ket.

\ ( e^{iπ}+1=0 \ )

\( e^{iπ}+1=0 \)

Yesterday evening I measured the temperature of a cup of hot water cooling over a 1 hour time period. I then tried to fit an exponential decay curve (to a background temperature of 21°C) and a quadratic curve to the data: the values of R² agreed to 4 dp!

https://pbs.twimg.com/media/EE0CyujXoAAnokp?format=jpg&name=small

-- https://twitter.com/mathstechnology/status/1174598153204637697

oops, just noticed I forgot to tag @11011110 in the above toot, for making that diagram. Follow him!

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