Wikipedia:Reference desk/Archives/Mathematics/2021 June 24

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June 24

Number 9

I have heard from a theology teacher about the nature of number 9. The teacher told that number 9 is a "number of divinity" because every mathematical aspects within universal realm produce number 9. For example, every whole numbers gives number 9 if they are multiplied by 9 and adding the product digits just like:

• 100×9= 900, 9+0+0= 9
• 6×9= 54, 5+4=9
• 2×9=18, 1+8= 9 ... And many more calculations.[1]

I don't know but you can explain it why number 9 is always dedicated to this and how numerologist responded it. The Supermind (talk) 21:08, 24 June 2021 (UTC)

• See Divisibility rule. Georgia guy (talk) 21:37, 24 June 2021 (UTC)
• Or Casting out nines (no relation to Casting out demons). The section Casting out nines § How it works also offers an explanation. Using modular arithmetic and the fact that the base of decimal notation 10 ≡ 1 (mod 9), this is mathematically almost trivial. It works in any base if you replace the digit 9 by the highest digit in any positional number system, so using hexadecimals you'd be casting out Fs. For example, B×F = A5, A+5 = F. So, in this context, the only thing that is special about 9 is that it is the value of 10 − 1 in the decimal system.  --Lambiam 21:52, 24 June 2021 (UTC)
• 0 is a whole number, 0×9 = 0. That's not 9. 11 is a whole number, 11×9 = 99, 9+9 = 18. That's not 9. The actual rule is that you start with a positive integer and you keep adding the digits as long as there is more than one digit. 1+8 = 9. PrimeHunter (talk) 23:52, 24 June 2021 (UTC)

@PrimeHunter: No I mean natural numbers and the above example of 11×9 = 99, 9+9 = 18, gives nine as you add 1 and 8. The Supermind (talk) 04:23, 25 June 2021 (UTC)

I get your point, but be aware that the natural numbers can include zero, and do so in many modern definitions. --Stephan Schulz (talk) 13:56, 27 June 2021 (UTC)

So why do we always learn that 0 is neither positive nor negative?? Georgia guy (talk) 15:31, 28 June 2021 (UTC)

I don't know why you always learn this, but in particular I don't know why it is relevant. Natural numbers don't have to be positive (and they are definitely not negative). The two definitions correspond to positive integers (excluding zero) and non-negative integers (including zero), but normally you start definition of the number hierarchy with the natural numbers and then extend the number space. --Stephan Schulz (talk) 20:25, 28 June 2021 (UTC)

If you were French or Belgian, you might learn that zéro is both positive and negative.  --Lambiam 22:06, 28 June 2021 (UTC)

• The number nine has this property because we're using a base ten system (Hebrew numerals are also base-ten). For example, if we used the hexadecimal system (base sixteen), we wouldn't be casting out nines, but fifteens. 78.0.133.114 (talk) 22:52, 26 June 2021 (UTC)
• That is not a property of 9, but a property of ([your counting system base] minus one). Had people widely adopted the octal system instead of decimal the number SEVEN would appear 'divine' instead of NINE, and if we were counting in hexadecimal the divine number would be FIFTEEN. But it's hardly acceptable the 'divinity' property should depend on a human's choice of their numeral system's base.
  Conclusion: let your theology teacher teach theology and stop listening to arithmetic absurds he tries to use to make you an idiot. --CiaPan (talk) 20:33, 27 June 2021 (UTC)

  Please do not jump to conclusions. A theology teacher does not have to be the OP's theology teacher. In fact, the use of the indefinite article in the original question suggests the opposite and does not warrant the conclusion that the OP lets themself be taught by any theology teacher. And rather than accepting their drivel, they came here to seek a maths-based explanation (and thereby, implicitly, a rejoinder).  --Lambiam 13:06, 28 June 2021 (UTC)

I didn't realise it: it was just so funny the voice saying, "number nine"; it was like a joke, bringing number nine into it all the time, that's all it was. (Lennon quote found in Revolution 9 § Structure and content).  --Lambiam 13:06, 28 June 2021 (UTC)