This is a little something I found interesting. I was at work waiting for further instructions and thought about numbers. I came upon this concept and started playing around with it.

The concept goes like this;

0 = 10
1 = 9
2 = 8
3 = 7
4 = 6
5 = 5
6 = 4
7 = 3
8 = 2
9 = 1
10 = 0

* An example would be the multiplication of 7 in multiplication of 10 would equal to the multiplication of 3.

Like this example;

7 -> 10 = 3
14 -> 20 = 6
21 -> 30 = 9
28 -> 40 = 12

etc... You can add or subtract to get the number in between the digits. All the other numbers are resulting in similar fashion. If you add a zero to your ten like 10 into 100, you must add a zero to your single digits. 2 will be 20, 5 will be 50, and so on.

The concept is done by the tens, hundreds, thousands, ten thousands, hundred thousands, millions, ten millions, and all the way up in tens. If you're using the concept in one million, then the single digits of 1 - 9 will have to be in the hundred thousands place. 0 will always equal to your greatest ten. 0 = 10, 0 = 100, 0 = 1,000, etc.

Try the same concept in other ways like 76 in 106 or something.

76 -> 106 = 30
152 -> 212 = 60
228 -> 318 = 90

The concept is still the same but in the tens place.

What do you think?

I was thinking of sharing this with some of you. It isn't relevant to anything special.

In a good part of my line of work thoughts like these are quite relevant.

It is always an interesting way to encrypt certain data, one way or the other, and could come in quite handy.

But I would say this; make it with ascii

So in other words, if your original number is n, then your new number is 10-n.



So in other words, the multiples of 7, subtracted from the multiples of 10, give you the multiples of 3. 10m - 7m = 3m. I'm not sure what you mean by "You can add or subtract to get the number in between the digits".


Again, this collapses down to the simple algebraic relation 106m - 76m = 30m. Am I missing something?

What I meant is that you can subtract 7 from 10 or add from 7 to 10.

10 - 7 = 3, 7 + 3 = 10 so multiples of 7 -> multiples of 10 = multiples of 3.

Besides that, yeah I think you're on the right track.

But 10m - 7m = 3m is algebraically equivalent to 7m + 3m = 10m. Maybe I'm missing something, but you just seem to be playing around with what in basic algebra is called the distribute rule, a(b+c) = ab + ac.

Not that number playing can't be fun or interesting. But it's also fun to realize why something works, IMO.

Thats fine.

Yeah I was pretty much playing with numbers.

What was interesting to me was that if you give a single digit multiples of 1 - 9 and compare it to the tens place like 6 in 10 you would get the multiples of 4. It would also apply the same if given 6,000 in 10,000. Do the multiplication of both multiples to equal the mulitplication of 4,000.

If you even do let's say 7,000,000 in 10,000,000, you would get the multiples of 3,000,000.

The concept stays the same regardless what the highest ten is but all other numbers under the highest ten must have an extra 0 to that digit. Like 10 - 90 in 100, 100 - 900 in 1,000, etc.

What struck me as being most interesting was the fact that you can find the multiples of the digit found in between those numbers. That was basically the idea.

Nothing wrong with that! I do it all the time myself.


This is basically the same as multiplying that equation I wrote earlier on either side by 10^n, for some integer n.

As long as we're talking about mathematical oddities, here's one of my favorites:
1*1 = 1
11*11 = 121
111*111 = 12321
1111*1111 = 1234321
11111*11111 = 123454321
etc.

There's also plenty of stuff out there based around the number 9, reinforcing the point Dr. LaVey made about the number in The Satanic Rituals.

I need to try that concept out. I'll be back for more later.

HS!

I find it a little weird. It is a simple, cryptographic if you will, conversion of numbers, but it looks to treat radix 10 as if it were radix 11. You might find this fun to play with differently.

First, nominate an extra digit:

0 = 0
1 = 1
2 = 2
3 = 3
4 = 4
5 = 5
6 = 6
7 = 7
8 = 8
9 = 9
10 = A

From this, the number 20810 would be 17A11. Zero is still the place holder in this case; 20910 is 18011.

Now, reverse it, as you did in your original cypher:

0 = A
1 = 9
2 = 8
3 = 7
4 = 6
5 = 5
6 = 4
7 = 3
8 = 2
9 = 1
10 = 0

Would 20810 be A71R11? Nope. That would be the same as 71R11, less the insignificant leading A (0). Let's see...

208 / 11 = 18 and 10/11
18 / 11 = 1 and 7/11
1 / 11 = 0 and 1/11

1-7-10 -> 930R11

Okay, let me check my work:

0 = 0
1 = 1
2 = 2
3 = 3
4 = 4
5 = 5
6 = 6
7 = 7
8 = 8
9 = 9
10 = A

208 / 11 = 18 and 10/11
18 / 11 = 1 and 7/11
1 / 11 = 0 and 1/11

1-7-10 -> 17A11

Then, reverse it:

0 = A
1 = 9
2 = 8
3 = 7
4 = 6
5 = 5
6 = 4
7 = 3
8 = 2
9 = 1
A = 0

17A11 = 930R11

The weird properties of your number game stem from the fact that you are not accounting for the change in radix that you introduced in your cypher. That is why your zeros grow in number faster than they should.

Here's one that's been bothering me for a little while.

If 1=1/1 or 2/2 or 3/3 ...

Then 1=3/3=1/3+1/3+1/3

1/3=.333333...

therefore

1=.999999....

Any explanations for this one guys?

That's correct. This argument comes up on Yahoo Answers every now and then, and there are always some people who refuse to believe it. But it's true. "0.999..." (with the nines repeating forever, as denoted by the ellipsis) is exactly equal to 1. Not "approximately", but exactly equal. They're two different ways of writing the same exact value.

There are a couple of other different ways to prove this. The simplest explanation is that there simply is no value you can write that falls in between those two numbers, so the two values are the same. These pages give some more explanations:
http://mathforum.org/library/drmath/view/55746.html
http://mathforum.org/library/drmath/view/55748.html

Math sure is a beautiful, elegant, and complex thing.

I always enjoyed how the 9's multiplication table is a mirror of itself after 9x5,meaning you just reverse the numbers and there's your answer
9x1=09
9x2=18
9x3=27
9x4=36
9x5=45
9x6=54
9x7=63
9x8=72
9x9=81
9x10=90

And, that if you add the digits of those multiples, the sum is 9. That property can be used to interesting effect.

Ask someone to give you a five digit number. Suppose he or she gives you 34769. Then, you tell them you are going to predict the sum of that number and four other numbers, writing down 234768 without him or her seeing it.

Then ask for another number. Suppose he or she gives 72231. The tally would appear as such:

34769
72231

And, you quickly add to the tally, 27768:

34769
72231
27768

Then ask for another. Suppose it is 40129:

34769
72231
27768
40129

And, you quickly add to the tally...

34769
72231
27768
40129
59871

Add them up, and you get 234768. This impresses the hell out of kids at least, but all you did was take the first number given, subtract 1 from the least significant digit, and add 2 as the most significant digit. Then, for each additional number you asked from your party, you quickly wrote down its nine's complement. Add them up, and it appears that you either used magic or you are much faster at adding than most people.

It can work with any number of digits, too, though the trick is easiest to do with all numbers being the same amount of digits.

I just noticed that if you go down the left (tens) column from top to bottom the digits go from zero to nine in order. Then go back up the right (ones) column starting from the bottom and these digits do the very same thing! Nines are just weird.

This is just a quirky function of our base-10 number system. It happens in any place-value notation of base n for the multiples of n-1.

Also, if you take the digits of multiples of n-1 and add them together, and add the digits of the result together, and keep adding digits until you have a 1-digit number, it will be n-1.

Eg. In a decimal notation, n-1 is 9.
9x3=27, 2+7=9
9x11=99, 9+9=18, 1+8=9
9x987=8,883, 8+8+8+3=27, 2+7=9

In a hexadecimal (base 16) notation, n-1 is F (in hexadecimal; "15" in decimal).
Fx3=2D, 2+D=F
Fx11=FF, F+F=1E, 1+E=F ("11" in hexadecimal is decimal "17")
Fx3DB=3,9D5, 3+9+D+5=1E, 1+E=F

In binary (base 2), n-1 is 1. So this works for any number at all.
10, 1+0=1
11,010,101; 1+1+0+1+0+1+0+1=101, 1+0+1=10, 1+0=1.
etc.

And, to think this so-called "New Math" was far to much for the American public school system. The "base" or "radix" of a number system flies over the heads of many people, and important mathematical concepts go right with it: Math is simply a language. Numbers simply nominate a quantity. Having a base or radix--ten fingers or "digits", 0 through 9--just makes it a hell of a lot easier to see it than Roman numerals did. (Thank you, Arabs.)

I suppose now might be a good time to poll on recommended reading pertaining to math and numbers.

I found this clock on-line, which has each number expressed with 3 nines:



Not surprisingly, there were idiots getting into the whole 0.999... (repeating) = 1 debate, because it uses that to mark Seven. Again, there's no debate. When the nines are going off to infinity, the value is exactly equal to 1.

A lot of the people who were debating otherwise were, also not surprisingly, computer programmers. They're an example of people who erroneously think of "infinity" as actual number. It isn't. There is no "last" or "infinities" place in the decimal. Fortunately there were others setting them straight.

Regardless, I think it's a cool clock.

Speaking of modulus arithmetic, in numerology there's the common practice of adding up the numbers corresponding to a person's name, then adding the digits of the result together, and repeating until you wind up with a single digit. Mystics still go through all of this, when all they really have to do is just divide the original number by 9 and take the remainder (or if it's 0, set the result to 9). But...don't tell them that!

Multiples of 9 are also the underlying reason why this old on-line mind-reading trick works:
http://www.bored.com/mysticalball/index.htm

You can thank the IEEE for that computer programmer infinity thing, or the fact that computer science in general has not the mathematical foundation it once did. That could be a chicken/egg scenario.

And now, for some REALLY misleading math with the number 9:

I might buy the sign for $9 just because. That is breathtaking.

Do you think anyone jumped at that deal?

I believe that they can get in trouble from the Dept. of Weights and Measures for that sign. If the original price was $29.99 and they are saving $-9, then the item would cost $38.99 not $39.98. That is a $300 fine by the DofW&M in San Bernardino County. They better fix it quick.

That definitely belongs on failblog.