View Full Version : Absolute Value, Only Positive...Or Not?

maddiesapphire

03-13-2009, 12:41 AM

You know, absolute value, how it can't be negative?

So, it's on a number line, aka the x axis.

Doesn't that mean that you actually could have negative absolute value on the y axis? =S

I told that to my math teacher yesterday and he ignored me, but seriously, it actually makes sense...

If you don't understand it, read it over a couple of times and you'll get it eventually.

Hoshika

03-13-2009, 12:54 AM

The absolute value of a number is the distance between the number and zero.

For example, both 3 and -3 have an absolute value of 3.

The absolute value can't be negative because distance cannot be negative.

To think about it in a different way, count how many spaces a number is away from zero on a number line.

Both 3 and -3 are 3 spaces away from zero on a number line.

Hope that helps.

Game Over

03-13-2009, 01:36 AM

The absolute value of a number is the distance between the number and zero.

For example, both 3 and -3 have an absolute value of 3.

The absolute value can't be negative because distance cannot be negative.

To think about it in a different way, count how many spaces a number is away from zero on a number line.

Both 3 and -3 are 3 spaces away from zero on a number line.

Hope that helps.

Thats probably the best way to describe it. Like Hoshika said, you can't have a number be negative spaces from zero, that wouldn't make any sense.

maddiesapphire

03-13-2009, 02:46 AM

Yes, I know that absolute value can only be positive, but technically, it is only in one dimension because it is only on the x axis. Would it be possible to have a whole new dimension of negative absolute value on the y axis?

Ranma

03-13-2009, 02:48 AM

Yes, I know that absolute value can only be positive, but technically, it is only in one dimension because it is only on the x axis. Would it be possible to have a whole new dimension of negative absolute value on the y axis?

I really don't get what you are saying...

maddiesapphire

03-13-2009, 03:38 PM

I really don't get what you are saying...

Yeah, you might have to read it over a couple of times.

Just picture a number line. For absolute value, it's a number line, except there are no negatives; it's just the distance from zero. So technically, since the number line is on the x axis, you COULD have negative absolute value on the y axis, since it's in another dimension.... hmm, I'll try to upload a pic of what I'm talking about later.

Nirvash

03-14-2009, 06:31 PM

Yeah, you might have to read it over a couple of times.

Just picture a number line. For absolute value, it's a number line, except there are no negatives; it's just the distance from zero. So technically, since the number line is on the x axis, you COULD have negative absolute value on the y axis, since it's in another dimension.... hmm, I'll try to upload a pic of what I'm talking about later.

No, you couldn't do that with the term absolute value. Absolute value is the distance from zero. You cannot have a negative distance from zero. You'll start to understand when you get into geometry... >.>

Buizel410

03-15-2009, 01:55 AM

Yeah, you might have to read it over a couple of times.

Just picture a number line. For absolute value, it's a number line, except there are no negatives; it's just the distance from zero. So technically, since the number line is on the x axis, you COULD have negative absolute value on the y axis, since it's in another dimension.... hmm, I'll try to upload a pic of what I'm talking about later.

What picture? If I see it, I can explain why it's not negative absolute value.

If what you're talking about is a graph showing y=|x|, y cannot be negative because it is the absolute value of something (x). X, however, can be negative because it is stated nowhere in the equation that x=|x|.

Kenny_C.002

03-20-2009, 05:48 AM

Yeah, you might have to read it over a couple of times.

Just picture a number line. For absolute value, it's a number line, except there are no negatives; it's just the distance from zero. So technically, since the number line is on the x axis, you COULD have negative absolute value on the y axis, since it's in another dimension.... hmm, I'll try to upload a pic of what I'm talking about later.

No, because absolute value has only a single dimension. Adding an extra dimension onto it doesn't affect it, since it is still calculated through that single dimension.

Think of it similar to complex numbers. Any integer technically has a complex dimension, but adding the fact that this dimension exists doesn't change the fact that the vector never runs along the complex axis.

Tranquil Leafeon

03-20-2009, 06:10 AM

If it helps you, think of absolute value as in driving a car. You can go backward, and the odometer will still have the mileage go up. Take a look at this picture.

http://img25.imageshack.us/img25/3240/xandy.jpg

The car moves down, but the odometer goes up. You can't have negative distance, but you can have positive distance going backward (or in this case, going down).

Hope this helps.

Lord Fedora

03-26-2009, 01:09 AM

Y wil never be negative in the equation y=|x|. If you look at a graph of y=|x|, you see that it is essentially a v, with the axis point at (0,0). The line will never be below the x-axis, therefore y will never be negative. Basic proof via graph.

Ah Beng I the Pikabeng

05-24-2009, 10:29 AM

Here we go. (http://en.wikipedia.org/wiki/Absolute_value)

Technically, absolute value is not always positive, because 0 exists. It is, however, always nonnegative (never less than 0), even when it's that of a complex number.

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