The discussion centers on the implications of mathematics without the concept of zero. Participants argue that eliminating zero complicates basic arithmetic and algebra, as it serves as the identity element for addition and is essential for defining operations like division and polynomial equations. Historical references highlight that ancient civilizations, such as the Romans, managed without a numeral for zero, but modern mathematics relies heavily on its existence for clarity and functionality. The consensus is that zero is fundamental to mathematical operations and theoretical constructs.
PREREQUISITESMathematicians, educators, students of mathematics, and anyone interested in the foundational concepts of arithmetic and algebra, as well as the historical evolution of mathematical thought.
But we do even more by using the zero: light on - light off - radio on - radio off - pc on - pc off - ...aikismos said:We do modular math without zero every day.
..., 1 o'clock, 2 o'clock, ... , 11 o'clock, 12 o'clock, ...
Well, the question of the nature of 'use' and 'more' is debatable. But it bears reminding ourselves that the use of 0 to represent off is arbitrary. You can use a perfectly isomorphic Boolean algebra using 1 and 2 instead... :Dfresh_42 said:But we do even more by using the zero: light on - light off - radio on - radio off - pc on - pc off - ...
Any "placeholder" with the same properties as 0 is just using a different symbol for the same thing.Alanay said:You could use a placeholder
Have I written a zero after this sentence or not?or simply not write anything at all.
Really? What is 1-1? That is pretty simple math that can not be answered without 0 because 0 is the answer.You can do even the simplest of math without 0.
FactChecker said:Any "placeholder" with the same properties as 0 is just using a different symbol for the same thing.
Have I written a zero after this sentence or not?
Really? What is 1-1? That is pretty simple math that can not be answered without 0 because 0 is the answer.
When you say "math", I assume you mean more than just listing objects/states and that you want at least one algebraic operation on the set. The set of states "light on", "light off" does not have an algebraic operation. To include at least one operation, you might consider "change light". But then, two "change light"s in a row would give you "don't change light". And that is the zero in binary arithmetic.fresh_42 said:But we do even more by using the zero: light on - light off - radio on - radio off - pc on - pc off - ...
Whether you write it down or not, it exists and is the only correct answer to 1-1=?Alanay said:Calculating 1-1 does not require you to write it down. You can still calculate at least the simplest of math without 0 obviously, but since you say "Really?" it seams you don't believe that. Try 1+1 or 11+21...
FactChecker said:When you say "math", I assume you mean more than just listing objects/states and that you want at least one algebraic operation. The set of states "light on", "light off" does not have an algebraic operation. To include at least one operation, you might consider "change light", "don't change light".
Whether you write it down or not, it exists and is the only correct answer to 1-1=?
I mean it's hard to take this discussion seriously and don't think it has the slightest to do with math. As I mentioned earlier stripping the zero only leaves counting behind and puts as estimated 7,000 years back in time. Even the Babylonians had balanced sheets. And the signs for our ciphers date back even earlier to an unknown place in India.FactChecker said:When you say "math", I assume you mean more than just listing objects/states and that you want at least one algebraic operation on the set.
FactChecker said:Whether you write it down or not, it exists and is the only correct answer to 1-1=?
If you had one atom, and took one away, there would be zero (0) atoms remaining. That should seem "obvious to the most casual observer" as one of my old math instructors often used to say.Alanay said:Or we could leave it as undefined, this may take us further into the subject of physics. Could you have one atom and take one away from it. No.
I believe it does have to do with math, but I agree that it's hard to take this discussion seriously.fresh_42 said:I mean it's hard to take this discussion seriously and don't think it has the slightest to do with math.
Alanay said:It's something I've been thinking about recently, would math be simpler or way more complicated without 0?
1,2,3,4,5,6,7,8,9,11,12,13,14,15,16,17,18,19,21...
I've been trying to do some simple equations without 0, and with small numbers the results are usually the same. But would getting rid of 0 solve any problems, for example dividing 0 by 0. I'm not sure how much this has been thought about before and if there has been any reasoning why this would be a terrible idea so I'd like your guy's opinions on the matter.
Mark44 said:If you had one atom, and took one away, there would be zero (0) atoms remaining. That should seem "obvious to the most casual observer" as one of my old math instructors often used to say.I believe it does have to do with math, but I agree that it's hard to take this discussion seriously.
Hornbein said:You could give up on 0 if you don't mind giving up on subtraction. Addition only! Shows a positive attitude.
1-1=?
If a mathematical operation that works only sometimes is good enough for you, then it is good enough for you.Alanay said:3-2=1 and we have used no 0's. We have not gotten rid of subtraction.
At which point we would say that we took one atom away, leaving zero of them.Alanay said:Good luck taking 1 atom away from 1 atom. You could move 1 atom from a particular position in which you are calculating how many of those atoms are there, but that's probably it.