Indices (understanding)

[Probability]

I've been reading through indices and I'm not getting the understanding of one part of the number line.

[MATH]...2^{-3},2^{-2},2^{-1},2^{0},2^1,2^2,2^3...[/MATH]
[MATH]2^{0}=1[/MATH]
Am I completely getting this understanding wrong or is there a typo in this;

[MATH]2^{-1}=2^{0}\div2=1\div2=\frac{1}{2}[/MATH]
The reason for asking this is because I see [MATH]2^{-1}=\frac{1}{2}[/MATH]
How can [MATH]2^{-1}=\frac{1}{2}[/MATH] yet [MATH]2^{-1}=2^{0}which=1[/MATH]
I'm thinking that [MATH]2^{-1}=\frac{1}{2}[/MATH]is not equal to[MATH]2^{0}[/MATH]which =1.

Hence the equation;

[MATH]2^{-1}=2^{0}\div2=1\div2=\frac{1}{2}[/MATH] can't be correct can it?

 

[Deleted member 4993]

I've been reading through indices and I'm not getting the understanding of one part of the number line.

[MATH]...2^{-3},2^{-2},2^{-1},2^{0},2^1,2^2,2^3...[/MATH]
[MATH]2^{0}=1[/MATH]
Am I completely getting this understanding wrong or is there a typo in this;

[MATH]2^{-1}=2^{0}\div2=1\div2=\frac{1}{2}[/MATH]
The reason for asking this is because I see [MATH]2^{-1}=\frac{1}{2}[/MATH]
How can [MATH]2^{-1}=\frac{1}{2}[/MATH] yet [MATH]2^{-1}=2^{0}which=1[/MATH]
I'm thinking that [MATH]2^{-1}=\frac{1}{2}[/MATH]is not equal to[MATH]2^{0}[/MATH]which =1.

Hence the equation;

[MATH]2^{-1}=2^{0}\div2=1\div2=\frac{1}{2}[/MATH] can't be correct can it?

Why do you think:

[MATH]2^{-1}=2^{0}which=1 [/MATH] .......... That is NOT correct!

How did you deduce that?

 

[pka]

I've been reading through indices and I'm not getting the understanding of one part of the number line.

If \(x\) is any nonzero real number \(\large\bf x\ne 0\) then \(\large\bf x^{-1}=\dfrac{1}{x}\)

 

[Steven G]

I've been reading through indices and I'm not getting the understanding of one part of the number line.

[MATH]...2^{-3},2^{-2},2^{-1},2^{0},2^1,2^2,2^3...[/MATH]
[MATH]2^{0}=1[/MATH]
Am I completely getting this understanding wrong or is there a typo in this;

[MATH]2^{-1}=2^{0}\div2=1\div2=\frac{1}{2}[/MATH]
The reason for asking this is because I see [MATH]2^{-1}=\frac{1}{2}[/MATH]
How can [MATH]2^{-1}=\frac{1}{2}[/MATH] yet [MATH]2^{-1}=2^{0}which=1[/MATH]
I'm thinking that [MATH]2^{-1}=\frac{1}{2}[/MATH]is not equal to[MATH]2^{0}[/MATH]which =1.

Hence the equation;

[MATH]2^{-1}=2^{0}\div2=1\div2=\frac{1}{2}[/MATH] can't be correct can it?

Where does it say that 2^-1 = 2⁰??? You need to read the whole equation.

For example 7 = 5 + 2. You can NOT say that it says 7 = 5! You have to read the entire equation. The entire equation says 2⁻¹=2⁰÷2=1÷2. Which equal sign(s) is not correct?

 

[Probability]

I agree with you all, I think it is written down incorrectly in the book. I needed all your feedback's so that I was clear in my own mind that the book is wrong on this point. Thank you all for this.

 

[Deleted member 4993]

I agree with you all, I think it is written down incorrectly in the book. I needed all your feedback's so that I was clear in my own mind that the book is wrong on this point. Thank you all for this.

What was EXACTLY written in the book - that created all these brou-ha-ha?!

 

[Probability]

I've been reading through indices and I'm not getting the understanding of one part of the number line.

[MATH]...2^{-3},2^{-2},2^{-1},2^{0},2^1,2^2,2^3...[/MATH]
[MATH]2^{0}=1[/MATH]
Am I completely getting this understanding wrong or is there a typo in this;

[MATH]2^{-1}=2^{0}\div2=1\div2=\frac{1}{2}[/MATH]
The reason for asking this is because I see [MATH]2^{-1}=\frac{1}{2}[/MATH]
How can [MATH]2^{-1}=\frac{1}{2}[/MATH] yet [MATH]2^{-1}=2^{0}which=1[/MATH]
I'm thinking that [MATH]2^{-1}=\frac{1}{2}[/MATH]is not equal to[MATH]2^{0}[/MATH]which =1.

Hence the equation;

[MATH]2^{-1}=2^{0}\div2=1\div2=\frac{1}{2}[/MATH] can't be correct can it?

See above here^^^^^^^

Where does it say that 2^-1 = 2⁰??? You need to read the whole equation.

I'm not reading this incorrectly, it is clearly a mistake in the book's written example as shown above.

 

[Deleted member 4993]

See above here^^^^^^^



I'm not reading this incorrectly, it is clearly a mistake in the book's written example as shown above.

I still don't see it! Highlight it for us please!

 

[Probability]

[MATH]2^{-1}=2^{0}\div{2}={1}\div{2}=\frac{1}{2}[/MATH]

 

[Probability]

Looking back on what the author is trying to visually explain, I now think that the author is saying [MATH]2^{-1}=\frac{1}{2}[/MATH]
[MATH]\frac{1}{2}=2^{0}\div{2}=\frac{1}{2}={1}\div{2}=\frac{1}{2}[/MATH] if that makes sense.

I think the idea is to put a pivot in the centre like a see saw and at each end of the equation [MATH]\frac{1}{2} = \frac{1}{2}[/MATH]

 

[Dr.Peterson]

You still haven't shown that the book said anything wrong, or specifically where it says that "2⁻¹=2⁰".

If you were referring to "...2⁻³,2⁻²,2⁻¹,2⁰,2¹,2²,2³...", that says they are all different, not that any two are the same.

If you were saying it was wrong to write "2⁻¹ = 2⁰÷2 = 1÷2 = 1/2", maybe you have not learned to read this kind of equation, with multiple equal signs. What it says, in words, is "2⁻¹ is equal to 2⁰÷2, which is equal to 1÷2, which in turn is equal to 1/2". Each of these four entire expressions is equal to the others, and the second is 2⁰÷2, not just 2⁰. And since all four are equal, he is ultimately saying that the first is equal to the last: "2⁻¹ = 1/2".

Is that where you are confused? What it says is correct; but the way you are reading it may not be.

 

[Probability]

You still haven't shown that the book said anything wrong, or specifically where it says that "2⁻¹=2⁰".

If you were referring to "...2⁻³,2⁻²,2⁻¹,2⁰,2¹,2²,2³...", that says they are all different, not that any two are the same.

If you were saying it was wrong to write "2⁻¹ = 2⁰÷2 = 1÷2 = 1/2", maybe you have not learned to read this kind of equation, with multiple equal signs. What it says, in words, is "2⁻¹ is equal to 2⁰÷2, which is equal to 1÷2, which in turn is equal to 1/2". Each of these four entire expressions is equal to the others, and the second is 2⁰÷2, not just 2⁰. And since all four are equal, he is ultimately saying that the first is equal to the last: "2⁻¹ = 1/2".

Is that where you are confused? What it says is correct; but the way you are reading it may not be.

You are correct Dr.Peterson, it took me a while for the penny to drop, if you know what I mean. I wrote it out in the post before this one and advised I'd got to the bottom of my misunderstandings. Thank you for your explanation.