Facts about the number 0

[Kyng]

Just thought I would start a thread where we post facts about the number 0. The facts themselves don't need to be mathematical in nature; however, they should be clearly related to the number 0 in some way .

I'll start off with:

1) Any number added to 0 equals itself.

Yes, I know what you're thinking: "Duh". You're probably very familiar with this: 6 + 0 = 6; 27 + 0 = 27; -9 + 0 = -9; and this works for any other number you might choose . However, to a mathematician, this property makes 0 special: there's no other number which has this property (if you try to solve equations like "6 + x = 6", or "27 + x = 27", you'll always get "x = 0").

There's actually a piece of mathematical jargon to describe this property: 0 is said to be the "additive identity". (Similarly, the number 1 is said to be the "multiplicative identity": any number multiplied by 1 equals itself. There are other "identities" like this in other areas of mathematics, but that's a matter for another thread: this just seemed like a convenient way to introduce the mathematical concept of 'identity', i.e. "thing which leaves everything else unchanged" )

And now, a non-mathematical one:

2) There are eight railway stations in the Great Britain which have a Platform 0

These stations are: Cardiff Central, Doncaster, Edinburgh Haymarket, Gravesend, King's Cross, Rainham, Redhill, and Stockport. Usually, when this happens, it's because they added a new platform next to Platform 1, and they didn't want to re-number everything (i.e. the new platform becomes "Platform 1", the old Platform 1 becomes "Platform 2", and so on, with every platform number increasing by 1... which would have led to a lot of confused passengers and missed trains . Sometimes, the station staff decide it just isn't worth the trouble, so they call the new platform "Platform 0", and leave all the other platforms with their original numbers - which is much easier for passengers to deal with )

I've been to two of these stations myself (Cardiff Central and Stockport). However, in this video, transport enthusiast Geoff Marshall teams up with mathematician Matt Parker to visit all eight of them:



I'd hate to think how much this convoluted train journey cost him. I can't imagine it was £0.00 !!!

So, do you have any more to add?

[Pyrite]

Ooh, I actually vaguely remember laughing to myself about Platform 0 when I was at Cardiff Central. I have a colleague who lives in Doncaster so I may now have to ask him if he's ever been to Platform 0.

[Kyng]

Ooh, I actually vaguely remember laughing to myself about Platform 0 when I was at Cardiff Central. I have a colleague who lives in Doncaster so I may now have to ask him if he's ever been to Platform 0.

Nice . My first encounter with Platform 0 was at Stockport (in 2009, when I changed trains there on my way to Sheffield), and it did seem a bit odd (although, it was quite a nice platform: it was still fairly new then, having been opened in 2003).

As for Rainham, which is another of the stations with a Platform 0... there's another curious zero-related fact about that same town:

3. The candidate who got 0 votes

During the 2015 local elections, Paul Andrew Dennis for Rainham North, and... he got zero votes. As far as I'm aware, that's the only time that's happened in any election for as long as I've been following politics.

Of course, Dennis wasn't willing to accept this result: he claimed he voted for himself, and his wife and his father also say they voted for him. The thing is, even if that's true, it'd still leave him well short of the 252 votes he needed to move out of last place !

[Kyng]

In case anybody's interested, the second half of the "Platform 0" journey is up now:



Apparently, Leeds might also be getting a Platform 0 in the near future. However, they might instead decide to just re-number all the platforms... they're not sure yet .

[Kyng]

When the Celsius temperature scale was first invented in 1742, the boiling point of water was set at 0°C.

No, that wasn't a typo . In the original version of the scale, higher numbers corresponded to colder temperatures - so, the freezing point of water was set at 100°C.

This version of the scale didn't last for very long: in 1743, just one year after the scale was invented, the numbers were reversed, so water froze at 0°C, and boiled at 100°C.

[Kyng]

6. 0/0 is undefined

What is zero divided by zero? You could argue that it should be 0, because 0 divided by anything is 0. Or you could argue that it's 1, because anything divided by itself is 1 . Or you could argue that it's undefined, because you can't divide by zero. So, which is it?

This short video gives a quick answer:



Basically, when you divide, you're doing the reverse of multiplication. So, when we do "20/5", we're asking ourselves: "How many lots of 5 will give us 20?". And the answer to this is 4 - because 4 x 5 = 20.

So... when we do 0/0, we're asking: "How many lots of 0 will give us 0?". But there's no one right answer to this question. 1 lot of 0 gives us 0; 2 lots of 0 gives us 0; 3 lots of 0 gives us 0; and indeed, any number of lots of 0 gives us 0 .

So, there's no such thing as "0/0".