# Is zero a cardinal number?

Discussion in 'Number Theory' started by in2infinity, Apr 20, 2022.

1. ### in2infinity

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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..

in2infinity, Apr 20, 2022
2. ### MathLover1

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The cardinal number of the empty set is is 0.

MathLover1, Apr 24, 2022
3. ### ddinunno

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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?)

ddinunno, Mar 31, 2023