# Questions tagged [number-comparison]

Tag for problems about comparing explicitly given numbers, often by hand calculation only.

92 questions
2answers
67 views

### Compare different base powers-towers (of 'height' five)?

Let's say I want to compare two numbers that are stacked powers of different bases: $a^{b^{c^{d^e}}}$ compared to $f^{g^{h^{i^j}}}$ where all ten values will be integers in the range $[1,10]$. ...
0answers
12 views

### Baseball: How are data sets with differing number of occurrences compared?

I have two data sets, each showing batting statistics for batters hitting against a specific pitcher. These tables show lifetime batting statistics of batters hitting against pitchers, therefore the ...
1answer
19 views

### Limit comparison test wrong equality

I am given the following comparison test question on my homework. Based on just plugging in the numbers, the first condition in all three answers is wrong, since it should say the original function is ...
1answer
44 views

### Comparing complex numbers with angles

Is $2 + i > 1 - i$ true? First off, what does it even mean to be "bigger" or "smaller" as a number? If we say that $a>b$ means that $a$ is on the right of $b$ on the number line, could we also ...
7answers
167 views

### Show that $19^{31}>13^{33}$

How can i prove that $19^{31}>13^{33}$? What I tried $$\bigg(\frac{19}{13}\bigg)^2=\frac{361}{169}>2>1$$ then $19^{2}>13^{2}$ and $\displaystyle 19^{30}>13^{30}$ How do I show it. ...
1answer
25 views

### Proof lower bound of $\lceil{n/2}\rceil$ comparisons for finding smallest and second smallest element

For a college assignment we are supposed to prove that a lowerbound of $\lceil{n/2}\rceil$ comparisons holds for a selection algorithm that finds the smallest and second smallest element in an ...
1answer
29 views

3answers
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### Which is greater, $\left(\frac{e}{2}\right)^\sqrt{3}$ or $(\sqrt{2})^{\pi/2}$? (no calculators)

From a math contest in 1985: Determine which of the following is greater: (no calculators) $$\left(\frac{e}{2}\right)^\sqrt{3} \, \hspace{3mm} \text{or} \hspace{3mm} \, (\sqrt{2})^{\pi/2}$$ Hints ...
0answers
19 views

### How to compare ratios of log values to obtain fold change differences?

I have some RNA expression data in the form of fold change. I have been trying to further analyze this data by making ratios of one value of another. These values have meaning in that a greater ratio ...
0answers
30 views

1answer
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### Which one is bigger? Logarithms and trigonometric functions

There's the problem: given that $0<\alpha<\beta<\frac{\pi}{2}$ , what is bigger $$\frac{\ln(\cos\alpha)-\ln(\cos\beta)}{\beta-\alpha}$$ or $$\tan(\frac{\alpha+\beta}{2})$$ I tried to ...
3answers
49 views

1answer
49 views

### GRE Question regarding two quantities

These are sample questions The question states this w > 1 ....Quantity A..............................Quantity B 7w - 4 .....
0answers
28 views

### Big O problem. Which one implies other?

Here $O$ means BIG-O. https://en.wikipedia.org/wiki/Big_O_notation If i am given with some data such that $$\|y_{\alpha}-x\| \leq O(\alpha^{\mu}) + O(\alpha^{\eta})$$ where $y$ is some variable ...
5answers
288 views

### Compare sum of radicals

I am stuck in a difficult question: Compare $18$ and $$A=\sqrt{7}+\sqrt{11}+\sqrt{32}+\sqrt{40}$$ without using calculator. Thank you for all solution.
5answers
200 views

### How do I compare $\sqrt{2}$ and $\pi^{1/ \pi}$?

How do I compare $\sqrt{2}$ and $\pi^{1/ \pi}$? I applied in calculator, I got $\pi^{1/ \pi}=1.4396194958475907$ and $\sqrt{2}=1.414213562373095$. So, $\pi^{1/ \pi} > \sqrt{2}$. How to show ...
1answer
53 views

5answers
2k views