Negative Zero

Division is a shorthand for subtraction. “6/3” is the number of times you can subtract 3 from 6 before you get to 0. Subtraction is a kind of addition too, just in the other direction (negative is the opposite vector direction to positive). 6/3 can also be expressed as the number of times you need to add 3 to itself (from 0) to get to 6. This is why computers only need “adders” to pull off all mathematical and logical calculations (or more precisely “half-adders”, which are just AND/XOR/OR gates in a specific arrangement to channel electrical current in a certain way to make the output look appropriately and usefully different depending on what you input).

To answer 0/0, how many times do you need to subtract 0 from 0, or add 0 to 0 to get to 0? Well you’re already there, but you can also do it any number of times, including an infinite number of times, meaning 0/0 is all numbers and no numbers - it’s undefinable. The “n” or “p” in your example are incidental, the “/” operation is what’s critical, or more precisely the “+” operation implied by"/". In this way, n/n and n/p are metaphysically the same.

“0 fitting into 1” is a kind of pie analogy that has the potential to be misleading - and you could also easily say that 0 never fits into 1. Or are you trying to imply that infinite is the same as never? That would leave you in a bit of a conundrum, if everything (infinity) was nothing (never) to you…

The clear way presents itself to those who understand where maths comes from, which I have described above. n/n when n=0 and and n/0 have no answer just the same way that paradoxes are just badly phrased questions that have no answer until you unpack them and find the internal contradiction that makes them invalid. There are many ways to categorise philosophers: an appropriate one for this situation might be to distinguish those that take on philosophy to solve internal contradictions in order to solve real problems (such as myself) from those who use philosophy as a means towards experiencing awe and mystery (such as Ecmandu and most female philosophers). The latter category gets nowhere with solving anything, instead they only further muddy and complicate things to stoke their imaginations. Whilst I support using your imagination, I do not support speculation for its own sake.

Thank you for making the effort to spell my name correctly. I know what you’re saying - it’s profoundly simple. It’s just wrong. I have further explained the role of the “negative” sign/subtraction above - it is more of a vector direction than a NOT, as I already explained and I’m sure you understand even if you won’t admit it. Negative 0 is just Positive 0 “but in the other direction” - that is to say they’re the same thing.

I already sussed you out, you don’t need to explain anything more to me. You want to play with definitions and see what happens. As I said, go ahead, hallucinate. Speculation can be a fun past-time and even lead back to utility in actual reality as long as you bring it back. Philosophy for the sake of philosophy has no end though, so just don’t expect me to play along like a fellow child. I’ll carry on trying to make reality better using truth with people who want the same instead.

And as I stated, it is not just a “not”, but an “everything but”

Let me clarify the convergence of not and negative at zero.

Not zero, implies other numbers, in order to abstract the distinction of zero for any conversation… the not operator solves as every number but.

Opposite of does not imply this except in the case of zero… zero is the lack of all number… which means that every number except zero is being referenced when zero is its opposite, both as other numbers existing as in the first proof, and everything but a placeholder has a place (negative: the opposite of)

I/0 is supposed to be infinity but that cannot be true because 0 times infinity is still only 0

This raises the interesting mathematical question of what if anything is greater than infinity

Assume for example that I/0 = X then what value would X have ? It would have to be infinity plus

That’s the thing though, negative isn’t “opposite of”, even at 0. NOT is. Negative is subtraction, which is “addition in the other direction”. Does opposite direction mean complete opposite? No. It’s still addition, not the opposite to addition. It’s only the vector direction that changes, the vector magnitude is the same ergo: not the complete opposite.

What is the addition of 0 in the other direction? Well the magnitude of 0 is the same, so direction (the only thing that distinguishes +0 from -0) doesn’t even matter at 0. You can go in any direction from 0 with 0 magnitude and you go nowhere. You remain at 0. -0 = +0 = 0.

!0 however? That’s the “opposite of” and it is every number but. The NOT operator is a binary operator, so when applied to 0, it’s what you’re trying to say -0 is: every number (but excluding 0). As in computing, any number other than 0 is “true” and 0 is “false”. True is the opposite of false, and 0 is the opposite of any other number than 0. Maths exists to straighten out the muddying that you can pull off with English, already solving problems like the one you’ve tried to come up with if you understand it. Yes, you can play around with definitions to see what happens, but what you want -0 to be is already accounted for by !0 so where you’re trying to get to has already been gotten to - it serves no purpose.

Oh, c’mon…

Negative 2 is not the subtraction of 2.

2-2 equals zero.

The distance as an opposite is 4!!!

It’s not subtraction, it’s opposite of

Oh, it really is :laughing:

That you don’t know this explains a lot about what you’re trying to do here.

2 is the addition of 2 from 0 = “0+2”. 0 is that same 2 but once you “-2”: the subtraction of 2 from 2, or the addition of 2 but in the opposite direction back from 2… to 0. It’s all very very simple.

What is “the distance as an opposite is 4” supposed to mean? 2-(-2) is 4, sure. How are you trying to misread me here?

I was a step ahead of you… 2 - (-2) is a double subtraction, which inverts what I said about subtraction itself. I’ll just forget that you ev n bothered to say subtraction is addition.

Opposite direction to the opposite direction is the same direction… so?

Like I said, don’t look to me for confirmation that subtraction is addition, just learn how computers work. Subtraction is addition… but in the opposite direction (same magnitude). Does that mean subtraction = addition?

Seriously, how are you misunderstanding me, maths and computers so badly? One step ahead? If ahead means in the opposite direction, sure.

Of course to subtract, you must be adding something…(duh) the subtraction, but this does not make the subtraction an added property in the sense that 2-2 = 4. 2-4 has a span of 4, rendering to 2 a zero, which can only happen with opposites, not with 2-4… can you understand that?

What? You think I’m saying subtraction is addition? That’s the only way 2-2=4, and that’s not what I mean. Be clear what you mean.

Span? What? You mean from 2 to -2 the magnitude moved is 4 because you -4? Obviously…

Can you explain properly, please? Then maybe you would make sense.

I addressed this in a previous post if you’ve not seen it yet.

Infinity plus isn’t really possible, but mathematicians like to see what happens if you denote an impossible concept and see if using it as a possible concept results in anything interesting or useful - such as complex numbers (e.g. “i”). But really, since you never get to infinity, you’re equally not going to get to greater than even that, so they’re the same concept. In case you’re not aware, infinity isn’t actually a number, it’s beyond numbers. You can’t really treat it like one, but like I said about mathematicians, you’re free to see what happens if you try. Just be prepared for results that make no sense and end in contradictions.

Like I also said, 1/0 isn’t infinity or infinity plus, it’s undefinable for the reasons I already explained. 1/0 is just an invalid expression: it doesn’t matter how infinite you make infinities, this remains true.

Subtract means to take away from so logically that can not be classed as addition
2 - 2 means 2 taken away from 2 not 2 added on to 2 before it is then taken away
A negative integer subtracted from a positive integer always leaves a smaller one

Ecmandu : 2 - 2 is both subtraction and opposite : subtraction because 2
is being taken away from 2 and opposite because - 2 is the opposite of 2

Nobody is saying 2 - 2 means adding 2 to 2 before taking it away. You just “add backwards” only: that’s the same as “taking away” - and you don’t do one and then the other!

It’s a matter of perspective. For example, In your computer a negative number is simulated by “wrapping” around at the mid point (known as the two’s complement). It goes from 0 to just before half the maximum number you can make from the number of bits you’re using, then it goes to negative half maximum number and ascends back to -1. But the bits themselves just look like they’re increasing the whole time. This cyclical interpretation of addition is how subtraction is derived in your computer - everything in your computer is derived from addition.

You might even think of addition like the magnitude moved, and subtraction as an afterthought on the direction you moved in respect to the number you started from. All of maths is addition with or without a twist on it. Note this is not saying that subtraction is addition, subtraction is addition in the other direction. If you swap which direction you’re thinking of as “increase”, then you’ll realise subtraction is just the opposite of whichever that direction happens to be - so long as you’re keeping everything consistent and swapping the direction of everything when you do so.

Subtraction, yes. Opposite? In direction, yes. But the magnitude is the same in each case (2). NOT is opposite in all respects, negative is only opposite in direction. Integers are scalars, with only magnitude, but signed integers (e.g. negatives) are vectors, which need both magnitude and direction. You’re thinking selectively, cherry-picking, to try and force this “NOT = negative” nonsense to appear to work. More likely though, you’re thinking ignorantly because you simply don’t have the education on the matter to realise where you’re going wrong.

Ahh yes the 1/ zero times = 1
Zero divided 1 time, is indivisible, so it just equals zero and not infinity or undefined.

It’s amazing how the elite have trained people to parrot stuff that cannot possible be true !

Like I said before, you didn’t use a negative to make your proof in the case of 2, you used a double negative. 2-(-2). So it’s not a proof of negative and shows that negative itself means opposite …,

What? Who said 1/0 = 1?

Nobody.

0/1? How many times do you need to subtract the denominator (1) from the numerator (0) until you get to 0? Well 1 is too much, because that gets you past your goal to -1. Half? Still the same problem. Only zero times gets you to 0. That’s why 0/1 = 0. 0/1 is defined, it is indeed not infinity nor undefined.
1/0? How many times to you need to subtract the denominator (0) from the numerator (1) until you get to 0? No number of times will ever get you lower than 1, not even an infinite number of times. Infinitely subtracting 0 from 1 still keeps you at 1. It’s an invalid expression, it’s undefinable, it’s not infinite, it’s not anything, not even nothing.

It’s amazing how the untrained or dumb (still not sure which of the two you are) make up stuff that cannot possibly be true without even realising, even when shown incontrovertibly what the truth actually is over and over.

You never did clarify whatever the hell you were on about with the double negative thing… how can I possibly comment on an imagined interpretation of what I didn’t say about a pile of nonsense that you came up with? I’ve demonstrated in several ways by now how negative doesn’t mean opposite. Opposite direction for a vector quantity (e.g. -2 compared to +2) doesn’t mean the complete opposite because the magnitude is the same. How are two things with the same magnitude the opposite? For the opposite, you need the NOT operator (jesus, how many times do I have to explain this?)!

Addition is a different operator than multiplication, multiplication is not addition squared. In the same sense division is not the same operator as subtraction, it is not subtraction squared.

The reason I point this out is because division is reciprocal to multiplication. If 1 is divided 0 TIMES!! It’s still one because it was never divided. If zero is divided 1 TIME, it’s still zero, because it’s not there to be divided.

I’ll be blunt with you.

We are speaking about different modalities of mathematics… yours is not linguistically salvageable, mine is.

Yet you accuse me of nonsense.

Addition squared? Subtraction squared?? What the hell are you on about now?!

What is the point of me explaining things if you either never read them/ignore them/forget them??

I already explained how division is derived from subtraction and therefore by addition, and in the same way multiplication is derived from addition. And no, you don’t need to “square” or “root” anything before you want to put any more nonsense in my mouth.
Multiplication is the amount of times you need to add something to itself to get to the answer e.g. 3x4 is 3 added to itself 4 times - that’s why it’s called 3 times 4.
Division is the amount of times you need to subtract the denominator from the numerator to get to zero (or add the denominator to itself to get to the numerator) e.g. 12/3 = subtract 3 from 12 to get to zero = 4 times or add 3 to itself to get to 12 = 4 times.
They’re all grounded in addition, and interestingly enough since you mention them - but probably beyond you, squares and roots also derive from addition too. This is literally how your computer works - the very thing you’re using to argue against the concepts that make it work… I’m not making this up, it’s very real and in your life everywhere. I’m using a different “modality”??? No, I’m just telling you what maths actually is and where it actually came from. You’re making up nonsense and putting nonsense into the mouth of others to try and make something ignorant and clearly flawed seem relevant.

I mean, here you are trying to say that 1/0 is 1. Yes you can use language to misleadingly represent something like division so it sounds like it doesn’t mean what it means. The word for this is Sophistry.

I rest my case, there’s no way you can salvage what you’re trying now with any amount of linguistics. Good bye.

So how do you multiply pi times the square root of 2 by your definition?

Bonus question: In the complex numbers, how do you show that i^2 = -1? How many i’s is that? How do you reduce this problem to addition?

Fortunately for computers the solution to multiplying irrational numbers is forcibly simplified by the number of bits you have to work with. Thereby, you apply the same reduction to addition that I explained to an approximation of said irrational numbers i.e. to a limited number of decimal (or binary in this case) places - as though they were rational numbers. To deal with (non-integer) numbers that have decimal points, variables of “float” or “double” type are used to represent numbers in an alternative way to allow more decimal places to be dealt with, even though the same number of binary places are being used - at the cost of accuracy. “Float” is short for floating decimal point, which hints at how the alternative representation manipulates bits to this end, although that’s not the only trick used. Still though, the limited number of bits nevertheless results in irrational numbers being dealt with as though they were rational - and the problem posed to mathematicians of irrational numbers is circumvented artificially.

Even outside of the world of computers, the same constraints are forced by practicality. Most vulgarly, for engineers and others who use irrational numbers in calculations that apply to everyday scales, the use of more decimal places quickly becomes redundant, meaning they too use irrational numbers like they were rational. But even for quantum physicists performing experiments at the quantum level, the use of more decimal places also becomes eventually redundant beyond a certain only slightly further threshold and the same truncation is resorted to - and everything still boils down to a twist on addition.

But what about for theoretical physicists and pure mathematicians? Their solution is even simpler: algebra. Got an irrational number? Use a letter to denote it (in exactly the same way that numbers denote integer quantities). This preserves the implied infinity of decimal places throughout all calculations, sometimes being cancelled out, sometimes being eliminated by certain properties of irrational numbers when used in, for example geometry. Consider that famous identity by Euler: “e^(pi)i = -1”. This equation is most simply shown on an 2D graph of a (complex) unit circle that plots its imaginary component against its real component, where pi is in radians and e is the base of natural logs as standard. Here we have 3 non-real numbers that when related to one another in a specific way amount to a real number, an integer no less.

Technically, “i” is just another kind of anomaly like irrational numbers that presents itself when building up maths from addition upwards - and to deal with that, in answer to your bonus question, the same solution of algebra is used. Mathematicians have to bring everything back into the realm of “boils down to addition” in order to deal with it - even the apparent exceptions that emerge from building maths in such a way. The whole point of maths is that it boils down to the simplest possible concepts, such that it is robust and consistent throughout.

In short: the practical solution is to truncate to a rational approximation, the theoretical solution is to use algebra.

Thank you for asking the first not-profoundly-stupid question in this thread for far too long.