The mystery of 9 and Infinite movement towards something.

salfriz

I have two questions which i wonder about from time to time and would appreciate any responses.

1 Why if you multiply 9 by any whole number and add up the reducing digets until they reduce to one diget will yo always get 9

ie: 9x43=387 3+8+7=18 1+8= 9

I cannot see the connection between the multiplication and the addition of digets. Do any other numbers behave the same?

2 Can something travel towards something forever but never actually reach it?
ie: the distance between two objects is 10 feet. Object x is stationary while object y begins to move towards it. In the first 5 seconds y moves 5 feet. In the next 5 seconds it moves 2.5 feet and in the next 5 seconds moves 1.25 feet. Y is moving towards X all the time but slowing down by half as it does so. Will Y ever actually reach X or travel beyond it?

There is probably simple enough solutions but i dont have them...so thanks for any responses an don't boggle your mind too much!

randombar

2, asymptotes, tan etc etc http://en.wikipedia.org/wiki/Asymptotically http://en.wikipedia.org/wiki/Tangent

nyarlothothep

I think 1 is because you're multiplying a number by 9, so the answer is a multiple of 9, therefore 9 is a factor and you will get 9 when you divide the multiple or add its digits. (I think, I'm not a maths dude so I don't know if this is right or not).

9x67=603
603/9=67
603/67=9

Joe1919

I'm not a mathematician and therefore am not going to try to give you a mathematical answer. However your second question reminds me of "Zeno's Paradox" and Aristotle's reply that infinity is only a concept (or limit or potentiality) and has no real "actual" existence. There is some merit in this answer. Your 10 foot can only be divided a finite number of times. Eventually the distance will be less than the width of an atom and therefore immeasurable and absurd.

salfriz

Joe1919 wrote: »

I'm not a mathematician and therefore am not going to try to give you a mathematical answer. However your second question reminds me of "Zeno's Paradox" and Aristotle's reply that infinity is only a concept (or limit or potentiality) and has no real "actual" existence. There is some merit in this answer. Your 10 foot can only be divided a finite number of times. Eventually the distance will be less than the width of an atom and therefore immeasurable and absurd.

Yes but an atom can be split and therefore halved. Even if is immeasurable by human measurements, there is still distance from one side to the other of it, ie: how many electrons would it take to cover the diameter and so on

Joe1919

"Definitions of atom on the Web: (physics and chemistry) the smallest component of an element having the chemical properties of the element."

It's still meaningless in terms of measurement of distance (in the conventional sense) once we get to distances smaller than the atom and there may be limitations in the Bohr model theory.
On the other end of the scale, there is the argument that space is also finite or has an outer area or limit.

The idea of infinity also creates some problems in maths.

Finally there the argument that eternal has a different meaning than infinity in terms of time and indeed for the inexistence of time in the first place.

I'm just suggesting that it is quite a plausible option that infinity is just a concept but does not actually exist in nature.

gondorff

nyarlothothep wrote: »

I think 1 is because you're multiplying a number by 9, so the answer is a multiple of 9, therefore 9 is a factor and you will get 9 when you divide the multiple or add its digits. (I think, I'm not a maths dude so I don't know if this is right or not).

9x67=603
603/9=67
603/67=9

With due respect, this sounds rather circular.

The reason why this happens is because we use the denary number system for counting.

If you start with 9 and add 9, you are essentially creating a 1 in the 'tens' column and subtracting 1 from the 9 in the units. This happens with each and every 9 which is added; 18+9, add 1 to the tens giving 2, subtract 1 from the units giving 7.

Kind of robbing Peter to pay Paul, to leave two digits whose sum is 9.

90,99,108 now a new 'hundreds' column is created, or you could call it ten tens and one eight... 117: eleven tens and one seven, and so on.
The unit is always taken from the right and moved along down the line towards the left.

You could say that 9+9=18 is axiomatic of the general rule.

Interestingly, if you take any number of any length, add up the digits in this number and subtract from the original, you are left with a number which is divisible by nine.

Maybe someone can explain to me why this is in mathematical terms.

bonkey

salfriz wrote: »

Yes but an atom can be split and therefore halved. Even if is immeasurable by human measurements, there is still distance from one side to the other of it, ie: how many electrons would it take to cover the diameter and so on

Planck Length, on the other hand, cannot be split.

IamBeowulf

1. Reminds me of the number 23. Apparently it shows up alot in day-to-day calculations. I'm not a mathematician but our number sequence is very limiting and can easily have repeating patterns.

2. Yes. I cannot think of any reason why any moving body cannot decrease its speed at an infinite rate.

Joe1919

" Yes. I cannot think of any reason why any moving body cannot decrease its speed at an infinite rate."

I can think of two answers to your statement.
1. According to Einstein, there is a maximum velocity that any mass or body can travel at (speed of light =300,000,000 meters per second). This would imply that the maximum change of velocity would be twice this (change from max in one direction to max in opposite direction.)
2. If your referring to acceleration, then there cant be infinite acceleration as this would need infinite force (and power). Force= mass X acceleration.

Even the sun has a limit to its power as well as a limit to its life in years if we believe modern science & big bang and all of that stuff.

bogwalrus

salfriz wrote: »

I have two questions which i wonder about from time to time and would appreciate any responses.

1 Why if you multiply 9 by any whole number and add up the reducing digets until they reduce to one diget will yo always get 9

ie: 9x43=387 3+8+7=18 1+8= 9

I cannot see the connection between the multiplication and the addition of digets. Do any other numbers behave the same?

2 Can something travel towards something forever but never actually reach it?
ie: the distance between two objects is 10 feet. Object x is stationary while object y begins to move towards it. In the first 5 seconds y moves 5 feet. In the next 5 seconds it moves 2.5 feet and in the next 5 seconds moves 1.25 feet. Y is moving towards X all the time but slowing down by half as it does so. Will Y ever actually reach X or travel beyond it?

There is probably simple enough solutions but i dont have them...so thanks for any responses an don't boggle your mind too much!

1: There are many symmetrical patterns in nature such as fractals and spirals that occur naturally, there is pii also. Mathematics is a tool used to understand these many naturally occuring patterns in nature and thus would mean that it too would have similar patterns, like the pattern of the number 9. Music would be another great example with the pattern of resonant harmonics on a taught string. The 3,5,7,12 etc

2: its all about infinity here. The way the human mind thinks about maths and this particular problem causes great confusion when infinity is involved in the equation. Where the experiment can seem to be quite linear and straight forward it is not and most humans will get confused on it=). Great for the head though if you can come to the conclusion without being told it is an infinity problem.