Understanding 0

[Larry Crain]

I am (obviously) not a math person but still have been trying to understand how 0 works such as x*0=0. This does not seem to me to be logical. 0 is not a number rather it represents the absence of any value - it is nothing. In physics when something is acted upon by nothing then nothing changes but in math when x is acted upon by nothing (x*0) then x disappears (x*0=0)? How does x become nothing when nothing has acted on it? By logic x+0=x, x/0=x, x*0=x and 0/0=0.

 

[kmcandy14]

It's not "acted upon", it means the value zero times, which is why the answer is always 0.
2 x 2 means 2 twice (4), 2 x 1 means 2 once (2),and 2 x 0 means 2 0 times, which is 0.

Does that make more sense?

 

[nycmathguy]

I am (obviously) not a math person but still have been trying to understand how 0 works such as x*0=0. This does not seem to me to be logical. 0 is not a number rather it represents the absence of any value - it is nothing. In physics when something is acted upon by nothing then nothing changes but in math when x is acted upon by nothing (x*0) then x disappears (x*0=0)? How does x become nothing when nothing has acted on it? By logic x+0=x, x/0=x, x*0=x and 0/0=0.

Zero is a digit and thus it is a number. A number without value but nonetheless a number. Your thread demands a deeper understanding of mathematics that I cannot help you with.

You said:

By logic x+0=x, x/0=x, x*0=x and 0/0=0.

x + 0 = x...correct.

x/0 is undefined not x. We cannot divide by 0.

x • 0 = 0. Zero times anything is nothing.

0/0 is not 0. It is called an indeterminate form.

Search online for a history of zero and real numbers.

 

[HallsofIvy]

"0" is defined as the "additive identity". That is, x+ 0= x for any number x.
We also have the "distributive law" for arithmetic: a(b+ c)= ab+ ac for any numbers, a, b, and c.

In particular a(b+ 0)= ab+ a0. But since b+ 0= b, a(b+ 0)= ab so ab= ab+ a0. Subtracting ab from both sides 0= a0.

 

[nycmathguy]

"0" is defined as the "additive identity". That is, x+ 0= x for any number x.
We also have the "distributive law" for arithmetic: a(b+ c)= ab+ ac for any numbers, a, b, and c.

In particular a(b+ 0)= ab+ a0. But since b+ 0= b, a(b+ 0)= ab so ab= ab+ a0. Subtracting ab from both sides 0= a0.

Original question dated 3/21/18.

 

[HallsofIvy]

And in all that time hadn't got a decent answer!

 

[conway]

And in all that time hadn't got a decent answer!

lol...that's because there isn't one! Unless you want to acknowledge zero is an empty dimensional unit. A dimensional unit without a numerical quantity.

 

[HallsofIvy]

Numbers, in mathematics, do NOT have units. It is quantities in specific applications that have. The number 0 is NOT the same as 0 meters, 0 seconds, or 0 degrees Celcius.
Mathematically, 0 is, as I said before, the additive identity.

 

[conway]

Numbers, in mathematics, do NOT have units. It is quantities in specific applications that have. The number 0 is NOT the same as 0 meters, 0 seconds, or 0 degrees Celcius.
Mathematically, 0 is, as I said before, the additive identity.

That is my point Halls. Numbers NEED units. The additive identity is a "property of zero". Not a description of what zero is.

If I asked you what a car was. You were to tell me "it gets you from (a) to (b)". You would be correct. Yet so to horses, bicycles, and scooters do the same thing. You cannot describe a "thing" by telling me what that thing does.

Also the "unit" applied to zero is not the same as a unit for concrete numbers. It is an abstract unit, not a concrete unit, and it is used differently.

 

[RobertSmart]

When we say "x times 0 equals 0," it's helpful to think of it in terms of groups. If you have zero groups of any quantity (represented by 'x' in this case), then the total amount you have is still zero. In other words, when you multiply any number by zero, you end up with zero because you have effectively "zero groups" of that number.

Regarding your statement that "0/0=0," this is actually incorrect. In mathematics, the expression 0/0 is considered undefined because it represents a situation where you're trying to divide nothing into nothing, which doesn't yield a definite answer. Division by zero is generally undefined in mathematics because it leads to contradictions and inconsistencies.

Similarly, "x/0" is also undefined because you can't divide any quantity by zero and get a meaningful result. Division by zero leads to mathematical inconsistencies and is not defined in standard arithmetic.

So, to clarify:

• x * 0 = 0 because you have zero groups of 'x'.
• x + 0 = x because you're adding nothing to 'x', so the value remains 'x'.
• x / 0 and 0 / 0 are undefined because division by zero is not defined in mathematics and leads to contradictions.

Understanding these principles helps maintain the coherence and reliability of mathematical operations, even if they might seem counterintuitive at first glance.

Grasping the fundamentals is not so easy. It require a lot of practice with samples and assignments. I would suggest you to visit mathsassignmenthelp website. for their samples and assignment solution. You can also contact them at +1 (315) 557-6473.

 

[conway]

When we say "x times 0 equals 0," it's helpful to think of it in terms of groups. If you have zero groups of any quantity (represented by 'x' in this case), then the total amount you have is still zero. In other words, when you multiply any number by zero, you end up with zero because you have effectively "zero groups" of that number.

Regarding your statement that "0/0=0," this is actually incorrect. In mathematics, the expression 0/0 is considered undefined because it represents a situation where you're trying to divide nothing into nothing, which doesn't yield a definite answer. Division by zero is generally undefined in mathematics because it leads to contradictions and inconsistencies.

Similarly, "x/0" is also undefined because you can't divide any quantity by zero and get a meaningful result. Division by zero leads to mathematical inconsistencies and is not defined in standard arithmetic.

So, to clarify:

• x * 0 = 0 because you have zero groups of 'x'.
• x + 0 = x because you're adding nothing to 'x', so the value remains 'x'.
• x / 0 and 0 / 0 are undefined because division by zero is not defined in mathematics and leads to contradictions.

Understanding these principles helps maintain the coherence and reliability of mathematical operations, even if they might seem counterintuitive at first glance.

Grasping the fundamentals is not so easy. It require a lot of practice with samples and assignments. I would suggest you to visit mathsassignmenthelp website. for their samples and assignment solution. You can also contact them at +1 (315) 557-6473.

Regarding the "additive identity". Zero is not "nothing".
Regarding the "multiplicative identity". (x) is not zero, therefore I still have "x". Multiplication does not make "x" disappear. Multiplication is addition.
Regarding "division" by zero. Please see thread "The Unified Number".

With just a little philosophy... mathematics, CAN make itself intuitive.

Thanks for your added kindness....