Thread: Inequalities

When using math induction on inequalities, I know we can drop positive values from the inequality without altering the meaning.

How can I word that better. I have wrote so far: Since $\displaystyle 2+2^k$ are both positive, we can drop them from the inequality without .....

How can I finish that sentence?

Thanks.

Originally Posted by dwsmith

When using math induction on inequalities, I know we can drop positive values from the inequality without altering the meaning.
How can I word that better. I have wrote so far: Since $\displaystyle 2+2^k$ are both positive, we can drop them from the inequality without ..... How can I finish that sentence?

Sorry, but as posted, your question does not make any sense.
Please post a complete question, not just fragments

My question has nothing to do with the problem but on how to word something; therefore, there is nothing I can copy from a book or problem set.

Example:

$\displaystyle 7<500\rightarrow 5+2<700$

We can drop the two and not affect the inequality.

$\displaystyle 5<700$

For this example, I might write, since 2 is positive, I can drop it from the inequality without .....

How can I finish that sentence.

If you know that $\displaystyle 0<2$ then surely $\displaystyle 5<5+2=7$.

Now what?

Originally Posted by Plato

If you know that $\displaystyle 0<2$ then surely $\displaystyle 5<5+2=7$.

Now what?

I am working on finishing a sentence correctly and have it make since. I am confused on why you are showing me ineqaulities.

Originally Posted by dwsmith

I am working on finishing a sentence correctly and have it make since. I am confused on why you are showing me ineqaulities.

I am confused why you think that sentence needs completing?
BTW: you mean sense

For this example, I might write, since 2 is positive, I can drop it from the inequality without .....

(1) breaking it; (2) making it false; (3) violating it; (4) changing its direction.

I know we can drop positive values from the inequality without altering the meaning

We can drop positive summands from the lesser side of the inequality.