favorite numbers: infinity and 7560

[Didymus]

So, two simple questions:

 

Reading a book by terry goodkind called the law of nines.... So I'm in a math mood. He mentioned that the sale of his paintings fetched him 14,400 and I was like 0o, that's divisible by 9, maybe that's important... Then I went off on a tangent thinking it's also divisible by 10 and 3, obviously.... And 2, therefore 6, and 1, of course.... And 8.... and 4.... But not 7....

 

So I tried to think of the lowest number I could that would be divisible by 1-10.... So it would have to end in 560 to cover 7,8, and 10... So I think 7560 is the lowest one.... Anyone know of a lower one?

 

Should this be the lowest one, it would entertain me enough to at least hold a place among my favorite numbers.... 0, OF COURSE, being my favorite, and infinity being my second....

 

So question 2.... I assume most people don't consider infinity a rational number? I've seen it debated a couple places

[Daedalus]

So I tried to think of the lowest number I could that would be divisible by 1-10.... So it would have to end in 560 to cover 7,8, and 10... So I think 7560 is the lowest one.... Anyone know of a lower one?

 

The number 2520 is the lowest possible number that can be divided by all the natural numbers 1- 10. To find this number, I took

 

[math]2^{a}\,3^{b}\,5^{c}\,7^{d}[/math]

 

and figured out the smallest exponent for each prime that would allow the numbers 1-10 to be a factor:

 

[math]2=2^1[/math]

[math]3=3^1[/math]

[math]4=2^2[/math]

[math]5=5^1[/math]

[math]6=2^1\,3^1[/math]

[math]7=7^1[/math]

[math]8=2^3[/math]

[math]9=3^2[/math]

[math]10=2^1\,5^1[/math]

 

You can see from the above results that the smallest number that has factors of 1 - 10 is

 

[math]2^3\,3^2\,5^1\,7^1=2520[/math]

Edited August 14, 2013 by Daedalus

[Didymus]

POOP! I derped and forgot to account for 10's hiding 7-8 pairs.... I hope my wife can forgive me.

[John Cuthber]

So, two simple questions:

 

Reading a book by terry goodkind called the law of nines.... So I'm in a math mood. He mentioned that the sale of his paintings fetched him 14,400 and I was like 0o, that's divisible by 9, maybe that's important... Then I went off on a tangent thinking it's also divisible by 10 and 3, obviously.... And 2, therefore 6, and 1, of course.... And 8.... and 4.... But not 7....

 

So I tried to think of the lowest number I could that would be divisible by 1-10.... So it would have to end in 560 to cover 7,8, and 10... So I think 7560 is the lowest one.... Anyone know of a lower one?

 

 

I can think of lots of lower numbers that meet that criterion.

All of them are zero or less.

[Daedalus]

I can think of lots of lower numbers that meet that criterion.

All of them are zero or less.

 

That's funny. I never thought about using zero or negative numbers. Of course, I tried to interpret the authors intent, but he didn't state that the number had to be a positive integer greater than zero. Positive rep to you for reading between the lines

[HalfWit]

 

That's funny. I never thought about using zero or negative numbers. Of course, I tried to interpret the authors intent, but he didn't state that the number had to be a positive integer greater than zero. Positive rep to you for reading between the lines

I'd say that's negative rep. "Number" obviously means "positive integer" in the context of the question. It's silly to say "OOh you forgot to say you're working in positive integers, gotcha gotcha."

[Daedalus]

I'd say that's negative rep. "Number" obviously means "positive integer" in the context of the question. It's silly to say "OOh you forgot to say you're working in positive integers, gotcha gotcha."

 

You are free to take a rep point away from John if you feel that way. Personally, I understand the satire of John's post. One of the biggest problems we have here on the forum is people do not clearly state their questions or answers, which leaves some ambiguity and can cause frustrations amongst other users. However, I also understand your point too, but it's always better to present your questions clearly. I believe John's intent was to encourage this deeper thinking when communicating (reading between the lines), and that is why I gave him the rep.

Edited August 14, 2013 by Daedalus

[Unity+]

I'd say that's negative rep. "Number" obviously means "positive integer" in the context of the question. It's silly to say "OOh you forgot to say you're working in positive integers, gotcha gotcha."

Actually you should be thankful to him. People would have misinterpreted your question.

 

Also, a number is a number. 0.5 is a number, as well as [math]\pi[/math] and other types of numbers. Number is not limited to positive integers. If you meant positive, integers just say positive integers.

[Didymus]

Thought about specifying "intiger" ... But I didn't want to sound snarky. As far as negative numbers go.... -8000 is still larger the +7000.... Just because it's on the other side of zero doesn't mean the number itself isnt larger.

[Daedalus]

Thought about specifying "intiger" ... But I didn't want to sound snarky. As far as negative numbers go.... -8000 is still larger the +7000.... Just because it's on the other side of zero doesn't mean the number itself isnt larger.

 

It depends on what you mean by larger. [math]-8000 < 7000[/math], but [math]\left | -8000 \right | > \left | 7000 \right |[/math] (assuming distance from zero or positive absolute value).

[John Cuthber]

Thought about specifying "intiger" ... But I didn't want to sound snarky. As far as negative numbers go.... -8000 is still larger the +7000.... Just because it's on the other side of zero doesn't mean the number itself isnt larger.

Feel free to increase both our bank balances by writing me a cheque for more than twice as much money as you have in your account.

(assuming, of course, that both bank balances are currently real and positive)

Edited August 15, 2013 by John Cuthber

[Didymus]

 

If I have $8000 in credit card debt and only $300 in my account, my debt is larger than my savings.

 

My -$8000 is larger than my +$300. Kind of like a small rock in a large hole. Just because a space is negative doesn't mean the volume isn't larger.

 

Even though -8000<300

 

It's all context.

Edited August 16, 2013 by Didymus

[Daedalus]

If I have $8000 in credit card debt and only $300 in my account, my debt is larger than my savings.

 

My -$8000 is larger than my +$300. Kind of like a small rock in a large hole. Just because a space is negative doesn't mean the volume isn't larger.

 

Even though -8000<300

 

It's all context.

Which is pretty much what I wrote:

 

It depends on what you mean by larger. [math]-8000 < 7000[/math], but [math]\left | -8000 \right | > \left | 7000 \right |[/math] (assuming distance from zero or positive absolute value).

[EdEarl]

My favorite numbers are 0 and 1, because they are binary digits on which all computers are based and the source of my work for many years. All numbers can be represented in binary, and the largest number divisible by a bit is 1, the analog to 2520₁₀. The largest address space, 2⁶⁴ is the integer analog to infinity for a computer, because it is the largest possible address on a 64 bit machine. Although, the largest floating point numbers are 128 bits, which can represent both plus and minus infinity, Of course, binary is not restricted to computers.

Edited August 16, 2013 by EdEarl