How is zero different from nothing? Should I travel beyond Earth's atmosphere I do not travel into zero but nothingness. What is the difference?
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How is zero different from nothing?
From a mathematical point of view, the answer is as follows:
Nothing is a set and zero is a number. Nothing is the empty set, i.e. the set with no elements. While zero is the cardinality of the empty set, i.e. the number of its elements.
Sets themselves are the objects of the mathematical discipline of set theory. They are the base of all other mathematical disciplines.
In addition, the number zero plays a fundamental role in structures like the additive group of integers:
x + zero = x
for any integer
Zero was not a number to the Greeks, since to them number was quantity, magnitude, or ratio, and the notion of e.g. a quantity of 0 is contradictory. A line of no length is not a line, by definition. To them number always meant number of something, and since nothing is not something, zero is not a number.
The fact that we treat zero as a number demonstrates that we no longer tie our concept of number to quantity etc. So zero does not mean "nothing", it's more of a structural concept, marking the point of symmetry between positive and negative. Of course you cannot have a negative quantity either, but you can have a deficit, and in fact our concept of zero originates with the people (Arabs or Persians working in Arabic) who invented algebra, which in its original form was mostly about balancing accounts, credits and debits. You need a zero concept to do that.
Space is not nothing. It has properties and can be described in terms of physical law. There cannot be properties associated with nothing.
Zero is a number. It tells you the quantity or value of some amount or property. Example: the net charge of an atom is zero.
It conveys information about whatever you are speaking about whereas nothing as its name implies conveys nothing.
In a setting where both are meaningful, the difference is pretty much just grammar. If I ask you how many apples you have on your desk, you have two choices:
- To give quantitative response: "zero"
- To reject the premise that there are apples on your desk: "none"
("nothing" is, I think, the wrong word to be comparing with "zero")
Natural language has developed in a way that prefers to use different language to distinguish between "zero" and "more than zero" (as well as "less than zero"). This is probably even a very good idea for the things natural language needs to be good at, although it gets in the way of trying to develop a concept that unifies the entire range of possibilities.
As the others have pointed out, nothing and zero have very distinct meanings in mathematics.
But from a philosophical perspective I am inclined to remember the saying "Space is the greatest thing as it contains all things" -- Thales.
That is, with nothing we able to experience something. That is not to say something comes from nothing, but nothing and something are the only absolutes, ( Think Epicurus ).
And zero is a measure of something that detonates a empty value, or attributes, or other. However, measuring nothing is not possible.
Zero is highly specific, not only mathematically, but in the English language. If for instance your GPS system is providing information as to the remaining miles to your destination: 3, 2, 1, 0, the zero is greatly appreciated, indicating that you have arrived. However if the GPS system says nothing, suddenly it is useless, providing no information. In information processing, binary bits of information we denote as 1's and 0's. There is no greater significance to a 1 or a 0, they merely indicate the presence or absence of a charge, a photon, magnetism, or some other proxy for a bit. They have a yin-yang relationship, both are equal and opposite, and both convey just as much information, however "nothing" conveys NO information. Another place where we really appreciate zeros in on our paychecks. A paycheck with zeros after a 1 is by far more desirable than one with nothing after the 1. Take your pick: $100000 or $1
I would regard "zero" as a number...as in "I was ejected into the nothing of space with zero...and died."
There are objects in Space but the vast amount is simply "nothing" is it not?
Meaning the absence of Air, the absence of light, the absence of anything "living" or "sentient" (as far as we know and within the confines of ability to see, observe, travel through and traverse in, etc)
So you can have "zero clothes on" but also be said to be "wearing nothing nothing." Yet are they one and the same?