Here's a question for satisfaction

Thread Starter

KevinEamon

Joined Apr 9, 2017
281
Say I was given a set formula to derive. Here's the circuit, make your equation look like "x."

But say I wanted to insert that into my "mathematical argument" (if that's the right expression?).
How would I say in math language - "in order to satisfy." You know like, before having yet proven, or derived anything.

It's really so I can refer back to the target equation, on my page, without constantly referring to the notes.
 

WBahn

Joined Mar 31, 2012
25,911
Say I was given a set formula to derive. Here's the circuit, make your equation look like "x."

But say I wanted to insert that into my "mathematical argument" (if that's the right expression?).
How would I say in math language - "in order to satisfy." You know like, before having yet proven, or derived anything.

It's really so I can refer back to the target equation, on my page, without constantly referring to the notes.
I'm not following what you asking close enough to give an answer. An example would help.

If you are generically asking how you can refer to an equation in your work, you can just give it an identifier. This is often done in the literature by putting an equation number in parentheses off to the right (although putting them on the left in handwritten work should be fine, too).

So then you can say, "In order to satisfy Eqn 4, we must...," or, "By using Eqns 9, 13, and 27, we can transform Eqn 38 into the following."

If you have many pages of notes, number the pages and then number the equations accordingly. So you might talk about Eqn 16-4 and know that it means equation 4 on page 16 of your notes.
 

Thread Starter

KevinEamon

Joined Apr 9, 2017
281
upload_2018-5-13_2-59-13.png
So here's the question. Now I want to put the equation, I'm kind of aiming for, at the top of my page. In my own handwriting in a simpler form. So I don't have to keep looking at this question, for my desired form.
 

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WBahn

Joined Mar 31, 2012
25,911
So here's the question. Now I want to put the equation, I'm kind of aiming for, at the top of my page. In my own handwriting in a simpler form. So I don't have to keep looking at this question, for my desired form.
I think I'm missing something here. Are you just asking how to annotate (mark-up) an electronic document?

If so, then there are lots of ways of doing it, ranging from using an app on a tablet PC to scanning your handwritten stuff (or taking a picture of it) and using any of a variety of image editing tools to paste it onto what you want.
 

Thread Starter

KevinEamon

Joined Apr 9, 2017
281
Well this sign, means => (Therefore) Right?

So...

I wanted some mathematical sign that meant... basically...
"In order for (xy+d/e=+fg) to be true

It's no problem it was just a curiosity. I'll just rewrite the question.
 

WBahn

Joined Mar 31, 2012
25,911
Well this sign, means => (Therefore) Right?

So...

I wanted some mathematical sign that meant... basically...
"In order for (xy+d/e=+fg) to be true

It's no problem it was just a curiosity. I'll just rewrite the question.
It depends on exactly what relationship you are looking for. Casual language tends to be quite ambiguous when used to express mathematical concepts.

You might be looking for necessary, sufficient, or necessary and sufficient depending on your purpose. Often times which one is meant is adequately established by the context, but not always.

To make this a bit clearer, let's consider a simple example of each (and hope that I haven't gone stupid on myself and picked a bad example where I'm missing something).

NECESSARY

In order for sqrt(z) ∈ ℕ to be true, x must be a nonnegative real number.

Notice that x being a nonnegative real number is necessary, but is not sufficient. This means that the only way that sqrt(z) can be a natural number is for x to be a nonnegative real number. It is thus NECESSARY that x be a nonnegative real number in order for sqrt(z) to be a natural number. But it is NOT sufficient; it is possible for x to be a nonnegative real number but for sqrt(z) to not be a natural number.

Said another way that is closer to an unambiguous claim:

IF sqrt(z) ∈ ℕ IS true, THEN x IS a non-negative real number.

Another way of writing this is

sqrt(z) ∈ ℕ is true ONLY IF x a non-negative real number.

This is called a material implication in logic and can be written as

(sqrt(z) ∈ ℕ) ⇒ (x ∈ ℝ) and (x ≥ 0)

SUFFICIENT

In order for sqrt(z) ∈ ℕ to be true, x can be any integer power of 100.

The constraint on x is sufficient for sqrt(x) to be a natural number, but it is not necessary. This is known as a converse implication and can be written as

(sqrt(z) ∈ ℕ) ⇐ (x = 100ⁿ) and (n ∈ ℕ)

Notice that we can write this as

(sqrt(z) ∈ ℕ) IF (x = 100ⁿ) and (n ∈ ℕ)

Also notice that we can flip this around and make it a material implication

(x = 100ⁿ) and (n ∈ ℕ) ⇒ (sqrt(z) ∈ ℕ)

which could be stated as

(x = 100ⁿ) and (n ∈ ℕ) ONLY IF (sqrt(z) ∈ ℕ)

which is a true statement in strict terms, although not something that we would usually mean in casual conversation.

NECESSARY AND SUFFICIENT

If we can state something like the following

In order for sqrt(z) ∈ ℕ to be true, x = y² and y must be a natural number.

Here we could express this as a necessary relationship or as a sufficient relationship and both would be correct, so we use the following notation

(sqrt(z) ∈ ℕ) ⇔ (x = y²) and (y ∈ ℕ)

This the implication goes both ways. If x can be written as the square of a natural number, then the sqrt(x) is a natural number and if the sqrt(x) is a natural number, then x can be written as the square of a natural number. This can be stated as

(sqrt(z) ∈ ℕ) IF AND ONLY IFF (x = y²) and (y ∈ ℕ)

which is usually shortened to

(sqrt(z) ∈ ℕ) IFF (x = y²) and (y ∈ ℕ)
 

Thread Starter

KevinEamon

Joined Apr 9, 2017
281
Thanks Wbahn. I think I'll be almost ready for this exam tomorrow. I'd love just one more day but it's not to be... ill have to make the most out of today. Thx guys for everything. Phone off, visor down, total study mode activated!
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;)
 
Last edited:

WBahn

Joined Mar 31, 2012
25,911
One thing that would help you enormously is to be more organized in your work. It's impossible to follow what you have done on that page with things written in little pieces everywhere, including across the top and down the sides. Imagine being a grader and having to grade that.

Plus, several of your equations are not dimensionally consistent.

Look at the top-left equation, for starters. In parentheses you have Rf/R3, which is dimensionless, added to VL, which is a voltage.
 
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