Can I invent my own version of mathematics?

[BenG549]

Did anyone still arguing with me actually read my original post?

 

[chiro]

For the people that say irrational numbers don't exist:

We could if we wanted to, designate that the standard base is SQRT(2) instead of 10 which means representing 10 in this case would end up being irrational and SQRT(2) would be rational in this base.

In fact, all languages have this property: In some bases you have an optimal language for an optimal representation and you also everything else that is not optimal.

In another language what was un-optimal in the other is optimal in this one and what was optimal in the other is un-optimal in this one.

Remember that the numbers themselves are just labels in some descriptive capacity and that descriptive capacity has advantages, disadvantages and limits to not only what it can describe, but more importantly how.

Many people forget that integer bases are not the only ones that are used for counting and for representation of numeric quantities.

 

[VantagePoint72]

I never said that negative numbers are useless because they're not real.

Sigh. No, but you're still saying they're not "real" (as in, don't really exist), while arguing that natural numbers are because they correspond to quantity. That's the inconsistency. I'm fully aware that you're not saying non-natural numbers are useless and I have you idea how you got the impression that's what I was saying.

Did anyone still arguing with me actually read my original post?

Yes. The original post that said:

Negative number don't actually exist per se, you can't actually have negative something, it is a physically impossible quantity, you can't physically have negative 1 banana.

If you genuinely don't see that what everything that has been said to you by various people is a direct response to this claim, then I doubt repeating it yet again is going to do it.

 

[BenG549]

Sigh. No, but you're still saying they're not "real" (as in, don't really exist), while arguing that natural numbers are because they correspond to quantity.

Yeah OK 'real' was a VERY bad choice of word on my part (especially given we are discussing mathematics), I guess I didn't mean real because that might suggest that I feel other mathematical ideas are fictional or that negative numbers do not exist on a number line and so on. I'm not saying irrational numbers etc don't exist... I've used them, I know they exist, but in the case of irrational numbers they are uncountable (Cantor's diagonal argument?.. someone with a maths degree might be able to qualify that) you can't observe an infinite series of digits or sets that is what I meant by not real (I accept that it was a bad word to use but in the context of my opening post I didn't think it was going to lead to this lol).

If you genuinely don't see that what everything that has been said to you by various people is a direct response to this claim, then I doubt repeating it yet again is going to do it.

Yeah, you're probably right. Thanks for trying anyway. Didn't mean to annoy anyone too much. I guess I should just concede that I'm either being wildly miss understood or too stupid to understand why I'm wrong, either way I should probably give up.

 

[BenG549]

Remember that the numbers themselves are just labels in some descriptive capacity and that descriptive capacity has advantages, disadvantages and limits to not only what it can describe, but more importantly how. Many people forget that integer bases are not the only ones that are used for counting and for representation of numeric quantities.

Exactly! This is what I've been trying to say.

 

[HallsofIvy]

Yeah OK 'real' was a VERY bad choice of word on my part (especially given we are discussing mathematics), I guess I didn't mean real because that might suggest that I feel other mathematical ideas are fictional or that negative numbers do not exist on a number line and so on. I'm not saying irrational numbers etc don't exist... I've used them, I know they exist, but in the case of irrational numbers they are uncountable (Cantor's diagonal argument?.. someone with a maths degree might be able to qualify that) you can't observe an infinite series of digits or sets that is what I meant by not real (I accept that it was a bad word to use but in the context of my opening post I didn't think it was going to lead to this lol).

That doesn't really mean much. You can't "observe" all of the digits in the decimal expansion of 1/3 either. But you can use "1/3" just as easily as "\sqrt{2}" or "e".

Yeah, you're probably right. Thanks for trying anyway. Didn't mean to annoy anyone too much. I guess I should just concede that I'm either being wildly miss understood or too stupid to understand why I'm wrong, either way I should probably give up.

 

[BenG549]

That doesn't really mean much. You can't "observe" all of the digits in the decimal expansion of 1/3 either. But you can use "1/3" just as easily as "\sqrt{2}" or "e".

Yeah I know that... believe it or not I've actually got a fairly good mathematical background through study of vibration engineering/signal processing/acoustics. The concept was actually something I picked up from one of my maths professors but it is clear that something has been lost in translation so I'm happy to concede that I'm not going to get anywhere with this lol.

 

[Whovian]

Is EXACTLY my point!

I can show you a tank with π cubic metres of water.

I can also find an electron and show it to you, and it has a charge of -1. Charge is just as real as, say, mass or volume.

Anyway, I've also gotten the feeling that some numbers aren't, in a sense, "natural" (in the sense that mathematics doesn't "think" in them,) but mine was the opposite of yours, trying to work with just integers seemed really ugly and unnecessarily discrete to me. And so I tend not to work with number theory.

 

[BenG549]

I can show you a tank with π cubic metres of water.

I can also find an electron and show it to you, and it has a charge of -1. Charge is just as real as, say, mass or volume.

Anyway, I've also gotten the feeling that some numbers aren't, in a sense, "natural" (in the sense that mathematics doesn't "think" in them,) but mine was the opposite of yours, trying to work with just integers seemed really ugly and unnecessarily discrete to me. And so I tend not to work with number theory.

As part of a process of reflection, I've read over this discussion again, and to be honest I don't really blame people for assuming me to be a bit of a crazy person, I definitely said a few things that could have easily been, and evidently were, taken the wrong way. Obviously I'm not going to argue that charge doesn't exist etc. things have definitely been blown a little out of proportion in this thread. I have no real problem with anything you guys are saying and I definitely regret even mentioning negative numbers lol.

 

[Whovian]

As part of a process of reflection, I've read over this discussion again, and to be honest I don't really blame people for assuming me to be a bit of a crazy person, I definitely said a few things that could have easily been, and evidently were, taken the wrong way. Obviously I'm not going to argue that charge doesn't exist etc. things have definitely been blown a little out of proportion in this thread. I have no real problem with anything you guys are saying and I definitely regret even mentioning negative numbers lol.

:) It's fine! I sort of get your point in that irrationals and such aren't "natural" (though I get the opposite feeling,) in which case you might want to go into number theory or combinatorics if you go into math.

 

[BenG549]

:) It's fine! I sort of get your point in that irrationals and such aren't "natural" (though I get the opposite feeling,) in which case you might want to go into number theory or combinatorics if you go into math.

To be honest that is part of my problem, I didn't even bring up the subject of irrational numbers or electrical charge, my original point had nothing to do with them lol, I just mentioned them in an attempt to defend myself when other people started quoting them at me as if I'd never heard of them before.. pretty much dug myself a hole in that respect I guess! I will look into those suggestions anyway though because I'll likely find some of the discussions interesting, much appreciated.

 

[WannabeNewton]

Does 1/10 count as an irrational number?

1 / 10 is a rational number...

 

[jtbell]

OK fine... Show me -$10.

My credit card balance right now is -$125.66. It doesn't show up with a minus sign on the credit card company's web site, but when I pay it off it will reduce my checking account balance.

 

[BenG549]

My credit card balance right now is -$125.66. It doesn't show up with a minus sign on the credit card company's web site, but when I pay it off it will reduce my checking account balance.

Slightly ignoring the fact that my comment about 'show me -$10' was borne out of confusing charges in an electromagnetic sense with charges in a banking sense, and running the risk of sparking up this debate again, when I said 'show me -$10' I was referring to the fact that you can't actually possesses less than 0 of any item, like dollar bills for instance, so the idea of negative quantities in this respect is just a conceptual way of explaining our reality. i.e. you owe 125.66 dollars, you don't actually have in your possession less than 0 dollar bills, you don't 'have' -$125.66.

And if you've suddenly thought of several reasons why that is a ridiculous thing to say then get in line lol. Although I think I've been put in my place enough, I accept that I'm probably talking nonsense.

 

[Evo]

Ooops, I forgot I was supposed to close this hours ago.