What Would Math be Like Without Zero?

[aikismos]

We do modular math without zero every day.

..., 1 o'clock, 2 o'clock, ... , 11 o'clock, 12 o'clock, ...

 

[fresh_42]

We do modular math without zero every day.

..., 1 o'clock, 2 o'clock, ... , 11 o'clock, 12 o'clock, ...

But we do even more by using the zero: light on - light off - radio on - radio off - pc on - pc off - ...

 

[aikismos]

But we do even more by using the zero: light on - light off - radio on - radio off - pc on - pc off - ...

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... :D

 

[FactChecker]

You could use a placeholder

Any "placeholder" with the same properties as 0 is just using a different symbol for the same thing.

or simply not write anything at all.

Have I written a zero after this sentence or not?

You can do even the simplest of math without 0.

Really? What is 1-1? That is pretty simple math that can not be answered without 0 because 0 is the answer.

 

[Alanay]

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.

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]

But we do even more by using the zero: light on - light off - radio on - radio off - pc on - pc off - ...

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.

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...

Whether you write it down or not, it exists and is the only correct answer to 1-1=?

 

[Alanay]

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=?

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 think) Your only reasoning to that would be if atoms could decay and how black holes are created.

 

[rootone]

I guess the earliest math dealt only with positive integers, which would have been useful enough for counting and trading purposes.
An empty trading stall can't trade anything, so from that point of view zero is a meaningless value, as the stall is out of business.
Also in construction projects, positive integers only would have been fine, a wall having no length is again meaningless.

 

[fresh_42]

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.

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.

I could understand if we debated the axiom of choice, the right of indirect conclusions or to go physics the entanglement or wave-particle-duality.
To drop us behind even finite abelian groups ... what's left then to call it math? And don't dare anyone to come around with that stupid esoteric Pythagoras.

 

[Mark44]

Whether you write it down or not, it exists and is the only correct answer to 1-1=?

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.

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 mean it's hard to take this discussion seriously and don't think it has the slightest to do with math.

I believe it does have to do with math, but I agree that it's hard to take this discussion seriously.

 

[Hornbein]

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.

You could give up on 0 if you don't mind giving up on subtraction. Addition only! Shows a positive attitude.

1-1=?

 

[Alanay]

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.

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.

 

[Alanay]

You could give up on 0 if you don't mind giving up on subtraction. Addition only! Shows a positive attitude.

1-1=?

3-2=1 and we have used no 0's. We have not gotten rid of subtraction.

 

[Hornbein]

3-2=1 and we have used no 0's. We have not gotten rid of subtraction.

If a mathematical operation that works only sometimes is good enough for you, then it is good enough for you.

 

[Mark44]

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.

At which point we would say that we took one atom away, leaving zero of them.

This thread has reached its maximum sillness level, so I am now closing it.