## Who is the greatest mathematician?

For you who is the greatest mathematician? This was a question asked to me by a kin, a freshman who is currently studying a  mathematics related course. This question is probably asked by many others who are just starting studying mathematics or those who are just simply curious.

Asking who the greatest mathematician is like asking who the greatest singer is. Singers have different genre that it is nearly impossible to tell. Pop lovers would probably suggest that it was Michael Jackson, but classical singers would probably disagree and would suggest some names like Luciano Pavarotti.

I think, determining the greatest mathematician is even more complicated than determining the greatest singer. Mathematicians lived in different times and the maturity of mathematics at different times is enormously different. For example, during the time of Euclid, it takes a high-caliber mathematician to prove that the inscribed triangle in a circle containing its diameter is right, while they can be easily proved by eighth graders of the present time. Of course, we cannot claim that our eighth graders are better than or even at the same level as Euclid because mathematics has changed so much.  Those who are only read by mathematicians during the time of Euclid are now taught in the elementary and high school levels.  In addition, mathematicians study different fields and it is impossible to compare the level of difficulty or even to quantify the effect of their contributions. » Read more

## Are all fractions rational numbers?

No.

A rational number can be expressed in the form $\displaystyle\frac{a}{b}$ where $a$ and $b$ are integers and $b \neq 0$. In other words, it is a fraction whose denominator is not zero, and both the denominator and numerator are integers.

Some fractions, however, may contain a numerator or denominator that is not an integer. Some examples of such fractions are

$\displaystyle\frac{\sqrt{3}}{2}$, $\displaystyle\frac{\pi}{4}$ and $\displaystyle\frac{e}{2}$.

A rational number may be represented in many ways, but it can always be expressed as a fraction. For instance, $10^{-1}$ is a rational number because we can express it as $\frac{1}{10}$. Also, the number $0.333 \cdots$, a repeating decimal, is  a rational number because we can also express it as fraction $\frac{1}{3}$.

## Are all objects with irrational lengths measureable?

I was deleting old emails a while ago and I came across with questions from some students reading my blog.  I have answered quite a number of questions from middle school and high school students via Email and Facebook since this blog started. I think some are worth publishing here, so I’ll probably post one from time to time.  Below is the first Q & A in this series.

Question

Are all objects with irrational lengths measureable?

Yes. In principle, they are measureable.

The number line represents all real numbers. It contains all the rational and irrational numbers.  In fact, there is a one-to-one correspondence between the set of real numbers and the set of points on the number line.  This means that every real number has a corresponding point on the number line, and every point on the number line has a corresponding real number. Therefore, since we can locate every irrational number on the number line, we can find its distance from 0.  This distance represents the irrational length.

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