Number Zero

mathxyz · 2024-05-21 20:55:03

The Mayans defined zero as the absence of value.

1. What is your definition of zero?

2. Why does zero times anything equal zero?

paulb203 · 2024-05-22 09:46:51

Why does zero times anything equal zero?

I guess x times y means how many lots of y you have

2 times y means you have 2 lots of y

10 times y means you have 10 lots of y

Zero times y means you have zero lots of y

You have no lots of y

You have no y

mathxyz · 2024-05-22 11:43:59

paulb203 wrote:

Why does zero times anything equal zero?
I guess x times y means how many lots of y you have
2 times y means you have 2 lots of y
10 times y means you have 10 lots of y
Zero times y means you have zero lots of y
You have no lots of y
You have no y

I get it.

What does the following mean?

Let 00 stand for infinity.

1. What is 0 • 00?

2. What 0 • -00?

3. What is 0 + 00?

4. What is 0 - 00?

Bob · 2024-05-22 19:51:48

3 and 4 are obvious. 1 and 2 ? Shouldn't really have these as infinity doesn't obey the four rules of arithmetic. But there could be a context where it makes sense

eg what is the value of x times 1/( x^2 + 2) as x tends to infinity. Here the method is to attempt to simplfy first.

As x^2 is getting very large the + 2 has a negigible effect so we can approximate the expression as x times 1/x^2 = 1/x

So we can see that, in this case, the expression tends to zero as x tends to infinity.

But there no general rule here; you have to simplify each expression separately.

eg (x^2 + 2) times 1/x gives a different answer.

Bob

mathxyz · 2024-05-23 08:34:55

Bob wrote:

3 and 4 are obvious. 1 and 2 ? Shouldn't really have these as infinity doesn't obey the four rules of arithmetic. But there could be a context where it makes sense
eg what is the value of x times 1/( x^2 + 2) as x tends to infinity. Here the method is to attempt to simplfy first.
As x^2 is getting very large the + 2 has a negigible effect so we can approximate the expression as x times 1/x^2 = 1/x
So we can see that, in this case, the expression tends to zero as x tends to infinity.
But there no general rule here; you have to simplify each expression separately.
eg (x^2 + 2) times 1/x gives a different answer.
Bob

Cool. Very good.

Phrzby Phil · 2024-05-23 08:57:29

For infinity discussion, I refer you to my post: https://www.mathisfunforum.com/viewtopic.php?id=31062

mathxyz · 2024-05-23 15:48:57

Phrzby Phil wrote:

For infinity discussion, I refer you to my post: https://www.mathisfunforum.com/viewtopic.php?id=31062

Thanks. Will do.

Math Is Fun Forum

#1 2024-05-21 20:55:03

Number Zero

#2 2024-05-22 09:46:51

Re: Number Zero

#3 2024-05-22 11:43:59

Re: Number Zero

#4 2024-05-22 19:51:48

Re: Number Zero

#5 2024-05-23 08:34:55

Re: Number Zero

#6 2024-05-23 08:57:29

Re: Number Zero

#7 2024-05-23 15:48:57

Re: Number Zero

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