Has It Ever Been Proven that One is Greater than Zero?

Through my endless philosophical thought, I realized something. I've never seen mathematical proof that one is greater than zero. Think about it. The entire number system revolves around the theory that one is greater than zero.

You could say, "If you had one dollar, and I had zero dollars, you have more money than me." However, the monetary system is also based on the theory that one is greater than zero.

Can anybody give me proof that one is greater than zero?

It really depends on what you're talking about. In some cases, 1 IS greater than 0, such as those you described.

In other cases though, 0 is better. In golf, a score of 0 is greater than a score of 1, for example. Even better than 0 are negative scores (-1, -2, etc.). It's just how the score system in golf works. Another example is just common sense. You'd rather have no bags of smelly garbage than one bag of smelly garbage, right? That's another example.

-4 -3 -2 -1 0 1 2 3 4

You're welcome.

Originally Posted by Palomino

It really depends on what you're talking about. In some cases, 1 IS greater than 0, such as those you described.

In other cases though, 0 is better. In golf, a score of 0 is greater than a score of 1, for example. Even better than 0 are negative scores (-1, -2, etc.). It's just how the score system in golf works. Another example is just common sense. You'd rather have no bags of smelly garbage than one bag of smelly garbage, right? That's another example.

But WHY is one greater than zero? Other than it's always been and we've based everything off of that theory?

Originally Posted by Bradley

But WHY is one greater than zero? Other than it's always been and we've based everything off of that theory?

My word, he's discovered the secret...

But really, I have to go with what Palomino said and label it as common sense. I have a rock. That other guy has no rock. I have MORE rock than him, as I have SUBSTANCE, he has nothingness in relation to rock matter. When I throw the rock into his skull at a high velocity, I would have committed murder with a rock, not the other way around. Know why? HE HAD NO ROCK. HE HAD ZERO ROCKS.

Originally Posted by Aura Pulse

HE HAS NO ROCK. HE HAD ZERO ROCKS.

He had zero rocks. He had 0 rocks. That's as many as no rocks.
And that's terrible.

Because Indians are cheap.


Seriously though, I don't think there is any mathematical proof past 1-1=0. It's like asking if 2 is greater than 1, or if 3 is greater than 2. That's the way the numeric system works and if you're really doubting it then have a look through a grade 1 math book.

Easy...

1 - 1 = 0
- 1 = o - 1
1 = 0 + 1

Originally Posted by Bradley

Through my endless philosophical thought, I realized something. I've never seen mathematical proof that one is greater than zero. Think about it. The entire number system revolves around the theory that one is greater than zero.

You could say, "If you had one dollar, and I had zero dollars, you have more money than me." However, the monetary system is also based on the theory that one is greater than zero.

Can anybody give me proof that one is greater than zero?

What is it you're asking? Because "one" is simply the name we give to a single discrete unit, while "zero" is the name we give to the absence of any discrete units.

So yes, by definition 1 is greater than 0.

Your problem is that you're, I think, asking for some objective proof that the way we've decided to label the universe is entirely correct, which doesn't exist, obviously.

I mean, I could apply the same criteria to your question: What does "greater" mean? Why? How do we know that greater means more of, instead of less? What about "than"? What does that mean? If something is "greater than" something does that mean we have more of it? Why? Why doesn't it mean we have less? etc.

It's all, forgive me, naval-gazing. Philosophy for the sake of philosophy. Thought that contributes nothing to our understanding of the universe.

Bradley, what is your definition of "greater"?

Mathematically speaking 1 is greater than 0, just as 3 is greater than 2. That is just how it is. If 0 for some reason would be higher than 1, the number zero itself would be useless.
But from a philosophical point of view, I would say 0 is greater than 1. Why? Because 0 is nothing, and nothingness itself is more or less eternal, while 1 is restricted to always be 1. Okay, that probably sounded very strange, but I really can't call myself a philosopher.

Why is 1 bigger than 0? The same reason 2 is bigger than 1. Because we said so.

My opinion, its just one of the kind of things that help us get on with our day like the idea that just because the color red is red, dont mean it couldnt be blue in someone elses eyes.

Originally Posted by Bradley

Through my endless philosophical thought, I realized something. I've never seen mathematical proof that one is greater than zero. Think about it.

This. This right here is exactly why I've had so much trouble with math over the years.

No matter what the subject matter is, I need to have everything make absolutely sense before I spend time on it or retain it. I don't do things "just because" somebody tells me to, and I don't learn things "just because" someone tells me that I need to know them. Why do I need to know it? "Because it's how the world works." Okay, but why does it work that way? I'm sure there is a detailed, logical explanation for math, but no one has taken the time to fill me in. It bothers me because math only appears to be logical and work if you have already agreed to play by the rules of math. It’s like a “which came first…” situation. If you agree to look at everything from within the rules of math, then everything makes sense. But why are the rules of math the rules of math? If it’s just a language, like any other language, then it doesn’t strike me as “the key to unlocking the universe” like mathematicians proclaim. Just like you said, what if I decide that zero is greater than one? Depending on where you are in the world, people make different sounds for the same thing, idea, etc. But if math is only the universal language because people haven't decided to use different “dialects” or languages altogether, then how or why is math considered the end all/be all? I NEED THE ANSWER!

Originally Posted by Nayru

This. This right here is exactly why I've had so much trouble with math over the years.

No matter what the subject matter is, I need to have everything make absolutely sense before I spend time on it or retain it. I don't do things "just because" somebody tells me to, and I don't learn things "just because" someone tells me that I need to know them. Why do I need to know it? "Because it's how the world works." Okay, but why does it work that way? I'm sure there is a detailed, logical explanation for math, but no one has taken the time to fill me in. It bothers me because math only appears to be logical and work if you have already agreed to play by the rules of math. It’s like a “which came first…” situation. If you agree to look at everything from within the rules of math, then everything makes sense. But why are the rules of math the rules of math? If it’s just a language, like any other language, then it doesn’t strike me as “the key to unlocking the universe” like mathematicians proclaim. Just like you said, what if I decide that zero is greater than one? Depending on where you are in the world, people make different sounds for the same thing, idea, etc. But if math is only the universal language because people haven't decided to use different “dialects” or languages altogether, then how or why is math considered the end all/be all? I NEED THE ANSWER!

something is always more than nothing no matter where you go or what language you speak. "One" and "zero" are just words we use to describe these concepts. One will always be more than zero because something will always be more than nothing. You can use whatever words you want but it will always be true. You can call "one" by the name "seven" and "zero" by the name "red" and the math remains the same. One is still more than zero, or using this language, seven is still more than red.

If I have something and you have nothing, I have more than you.

EDIT: Damn I post late.

Originally Posted by Lysis

something is always more than nothing no matter where you go or what language you speak.

But isn't the concept of "nothingness" constantly in question? From what I understood of physics, there is no such thing as a perfect physical vacuum. So wouldn't saying “something is more than nothing” only be correct when applying math to a very specific thing? Again, tweaking the language. Like I can say that zero is an absence of some specific thing, but not an all-encompassing "something." I can say "I have zero staplers" or "If I had 1 stapler, and I gave Martin 1 stapler, I would have zero staplers." But just discussing "zero" or "one" without assigning them to a thing leaves them with no meaning... ?

Originally Posted by Nayru

But isn't the concept of "nothingness" constantly in question? From what I understood of physics, there is no such thing as a perfect physical vacuum. So wouldn't saying “something is more than nothing” only be correct when applying math to a very specific thing? Again, tweaking the language. Like I can say that zero is an absence of some specific thing, but not an all-encompassing "something." I can say "I have zero staplers" or "If I had 1 stapler, and I gave Martin 1 stapler, I would have zero staplers." But just discussing "zero" or "one" without assigning them to a thing leaves them with no meaning... ?

zero is nothing. Whether or not nothingness is physically possible isn't relevant. Zero is a mathematical concept, not a physical one. Zero is mathematically possible, just as infinity is mathematically possible, or a perfect circle is mathematically possible, even though none of these things can be perfectly represented in physical form.

Originally Posted by Lysis

zero is nothing. Whether or not nothingness is physically possible isn't relevant. Zero is a mathematical concept, not a physical one. Zero is mathematically possible, just as infinity is mathematically possible, or a perfect circle is mathematically possible, even though none of these things can be perfectly represented in physical form.

I understand math as a basic set of rules. So I understand that within math itself "zero" makes sense and you can have "less than zero." It’s like playing a game. Beyond math for the sake of math, though, the rules don’t seem to apply or make sense to me. And math is used to describe the universe and everything in it. So when mathematics and the rules of mathematics are applied to physical things, etc., I don't understand how the rules of mathematics continue to function. I have trouble seeing how or whether the rules of the game ARE the rules of the physical universe, or if we are squeezing our perception of the universe to fit the rules of math that we are viewing the physical universe through. I honestly don’t know if I am able to articulate this.

Originally Posted by Nayru

I understand math as a basic set of rules. So I understand that within math itself "zero" makes sense and you can have "less than zero." It’s like playing a game. Beyond math for the sake of math, though, the rules don’t seem to apply or make sense to me. And math is used to describe the universe and everything in it. So when mathematics and the rules of mathematics are applied to physical things, etc., I don't understand how the rules of mathematics continue to function. I have trouble seeing how or whether the rules of the game ARE the rules of the physical universe, or if we are squeezing our perception of the universe to fit the rules of math that we are viewing the physical universe through. I honestly don’t know if I am able to articulate this.

mathematics describes numbers. Numbers are abstract. They're not physical objects. It is physics that describes the physical universe and physical things.

"As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality." - Albert Einstein