Is zero a cardinal number?

[in2infinity]

Hi there. I was having a real problem finding out is zero was a cardinal number or not?
This website says it is...

https://www.yourdictionary.com/cardinal-number

and this website says it is not?

https://byjus.com/maths/cardinal-numbers/

In fact the issue seems to be very unclear.

Zero is not in the ordinal set as there is no ZEROth step. Is that right?

I want to know is I am standing at zero, and a Take a step, Do I count the zero number, and is this a cardinal number?

I apologise if this seems like a very simple maths question. Thanks in advance for your help..

 

[MathLover1]

The cardinal number of the empty set is is 0.

 

[ddinunno]

The cardinal number of the empty set is is 0.

This is a frequent challenge in software program. It is said that, "programmers are often off by 1." - just for the type of issue you indicated. Where do I start?

Is "next Sunday" the one coming up or the one after that?

Is Maryland 1 state away from Virginia or - since they touch - is it 0 distance. Historically, some cultures would count Maryland as 1 and Virginia as 2. So, Virginia is two states away. (Of course, historically, Maryland and Virginia did not exist.) Also, historically zero did not exist.

I agree that while 0 is not a counting number it is the cardinality of the null set.

P.S. Historically 1 was considered a prime number. (How more prime can you get than 1?)

 

[conway]

I find this thread fascinating. The real issue is in how we define zero, and its cardinality. An empty "set" is the absence of a numerical quantity.

It is NOT, absent a dimensional unit quantity. It is this quantity that we should philosophically count, when we are standing on zero, and moving to 1 or negative 1.

Consider (1 + -1 = 0).

This is proof of the space of zero. Or the dimensional unit quantity.

This is also relative to how we define zero. It is currently defined as a "whole number". Yet numbers are defined as numerical quantities. Yet zero is the absence of a numerical quantity. Therefore logically it should not even be defined as a number.

Give zero a dimensional unit quantity. Along with all other numbers. Allow it to remain without a numerical quantity. And you can answer the above questions. As well as solve for division by zero.