Physicist97 said:Hello! What I'm wondering is if you want to prove an inequality, let's say ##a<b## and you already know that ##a>c## is true. If you are able to prove that ##c<b## is true, would that go on to imply that ##a<b## is true also? If this is correct, is it known as a theorem?
Thank you!
The process for proving inequalities true depends on the specific type of inequality being considered. In general, it involves manipulating both sides of the inequality using mathematical operations and properties until they are equal or one side is clearly greater than the other. This process may also involve using known theorems or properties of inequalities.
Yes, inequalities can be proven using only algebraic manipulations. However, in some cases, it may be necessary to use other mathematical tools or concepts, such as calculus or geometry, to fully prove an inequality.
To check if a proof of an inequality is correct, you can use the following steps:
Yes, there are a few common mistakes to avoid when proving inequalities:
Yes, inequalities can be proven using real-world examples or applications. In fact, many real-world problems and scenarios involve inequalities, such as comparing prices of goods, analyzing economic trends, and determining optimal solutions to problems. In these cases, the inequality can be represented mathematically and proven using appropriate tools and methods.