Math Questions

[Jeff-20]

I'm not the best math guy, but I asked a few friends and got different answers.

Problem 1: If you wanted to name all single digit multiples of 3, would you say 3,6,9? or 0,3,6,9? or just 6,9? I tend not to include zero, but the computer would. And one of my friends didn't even include three because she thinks of "multiples" as meaning beyond the number itself! Which is the best answer to you?

Problem 2: Prime numbers! Do you count 1? Would single digit prime numbers be 2, 3, 5, 7? or 1, 2, 3, 5, 7? Is zero not even considered because it's not a "natural number" ?

Finally, what is a quick way to make the VIC determine a prime number in BASIC?

[Kweepa]

I would say 3, 6, 9.
Then 2, 3, 5, 7,...
Sieve of Eratosthenes?

[wimoos]

When trying for a number to be prime there's no reason to test any further than the square root of that number.
When "even" is also ruled out then you have a pretty Q&D algo.

10 input x
20 if x/2=int(x/2) then (no prime)
30 for i=3 to sqr(x) step 2
40 q=x/i:if q=int(q) then (no prime)
50 next
60 (prime)

[Mike]

1. Whether 0 is counted to the natural numbers, or not, depends on your Maths professor.

At least the concept of zero is not quite self-evident: one might "naturally" count one, two, three, or more occurences of a thing, but it takes a fundamental abstracting step to name that no-thing of some kind is present: the Indian word for zero - sunya - means "empty".


2. Neither "0", nor "1" are counted as prime numbers. This is because any non-prime number (except 0 and 1) has an unique factorisation into a product of prime-numbers: for example - 2 x 5 = 10, 2 x 2 x 3 = 12, 5 x 7 = 35, ...

A permutation of factors (as in 5 x 2 = 10) is not taken into account, since multiplication is commutative.

If one would include 1, the above theorem would be false, since: 2 x 1 = 2, but also 2 x 1 x 1 = 2, 2 x 1 x 1 x 1 = 2, ... . And 0 cannot be included either, because 0 in a factorisation only can produce 0 as result.

Greetings,

Michael

[ravenxau]

3 is not a multiple of 3 - multiple implies at least 2 of something - therefore the first multiple of 3 is 6 (2x3=6) - also factors and multiples are only supposed to include whole numbers (I may be wrong on this, tho).

as for the rest, it's pretty open to debate (the best thing about theoritical maths, quantum physics..etc...)

[Mike]

Any number N that can be written as 3 x n = N, with n being a natural number is a multiple of 3. There's no good reason to exclude n=1, and n=0 from that list.

Of course it doesn't make any sense to allow arbitrary fractions, or real numbers for n, since that would make any number a multiple of 3.

As for this ...

as for the rest, it's pretty open to debate (the best thing about theoretical maths,

... Mathematics pretty much has settled on Peano's axioms defining the natural numbers for more than 100 years, which include 0 as neutral element for addition.

They're axioms and cannot be derived from anything. But they produce a faithful representation of how natural numbers "work" from a minimal set of assumptions:

1) 0 is a number,
2) every number has a successor,
3) 0 is not a successor of a number,
4) different numbers have different successors,
5) of all sets, that include 0, and with every number also its successor, the set of natural numbers is the smallest one.

The last axiom infers the method of Mathematical induction.

[gklinger]

Problem 1: If you wanted to name all single digit multiples of 3, would you say 3,6,9? or 0,3,6,9? or just 6,9?

I would say 0, 3, 6 and 9 because 3 x 0 = 0 and 3 x 1 = 3 and therefore both meet the condition set out in your question. Although not mentioned, -3, -6 and -9 would also seem to qualify, no?

Problem 2: Prime numbers! Do you count 1?

No. By the currently accepted definition 1 is not a prime number. Read up on the "primality of one" if you wish to understand why.

[pitcalco]

zero is not a prime number but not for the same reason as the number one, but quite simply that it can be evenly divided into any number. Zero divided by any number (except zero) is always zero. Conversely, any number multiplied by zero is equal to zero so it has an infinite number of factors.

[English Invader]

Radio DJ: Which sixties pop group was known as the Fab Four?

Butt-Head: Math was always my worst subject.

[Mike]

Zero divided by any number (except zero) is always zero.

Correct. The division by 0 - a 0 as nailed-on number, not a limit - isn't allowed anyway, regardless of the number being divided is non-0, or 0.

Michael

P.S.: This topic strikes me as not specifically relevant to VIC-20 programming, software, games, hardware, or trading. Maybe the OP could move it into the Off-topic section?

[Jeff-20]

It was just a personal programming issue. The vic doesn't use math the way I do. I would explain more but I'm typing ony iPhone because I am too far from people and civilization at the moment. The question will make sense later. Haha

[carlsson]

Are you implying the VIC-20 isn't the Friendly Computer after all?

[gklinger]

I would explain more but I'm typing ony iPhone because I am too far from people and civilization at the moment.

Geez. Vancouver isn't that bad.

[Mike]

I'm typing on my iPhone because I am too far from people and civilization at the moment.

It can't be too far away from civilization, since the text found its way to here. The need for using RFC1149 might be a better excuse.