What's a cool math fact you can easily tell a layman and look super cool?

 

• You can get any real number from $0$ to $\infty$ by using only four 4 digits$(4,4,4,4)$. For example
• $(4+4)-(4+4)=0$
• $(4÷4)÷(4÷4)=1$
• $(4÷4)+(4÷4)=2$
• $(4\times 4-4)÷4=3$, and son on…
• Click here for details

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• Look at this expression. ${(1+9^{-4^{6\times 7}})}^{3^{2^{85}}}$

• The above expression contains every digit from $1$to $9$
• Now take out a calculator and solve the expression. You will get approximately $\mathrm{2.718281828459.}$Which is value of $e$(Euler's number)

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• Magic of Digit $9:$
• Divide $1$ by $9^2$. You will get every single digit from $1$ to $9$ after decimal point except $8$.
• $\frac{1}{9^2}=0.012345679012345679\cdots$
• The missing number $8$ in the sequence is first digit of $81$ which is $9^2$
• Divide $1$ by ${99}^2$. You will get every two digit number from $00$to $99$ except $98$.
• $\frac{1}{{99}^2}=0.00,01,02,03,04,05,06,07,\cdots ,96,97,99,00,01,02,\cdots$
• The missing number $98$ is first two digit of $9801$ which is ${99}^2$
• Divide $1$ by ${999}^2$. You will get every two digit number from $00$to $999$ except $988$.
• $\frac{1}{{999}^2}=0.000,001,002,003,\cdots ,996,997,999,000,001\cdots$
• The missing number $988$ is first three digit of $988001$ which is ${999}^2$
• Isn’t it cool?

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• Infinity ($\infty$)
• When you think of infinity, the only thing that might hit on you brain is that the infinity is largest number. Well that is not true.
• When you move towards right direction on number line, you get closer to the $\infty$. While, when you move towards left, you again get to $\infty$. Most people think that the infinity is infinity, whether it on left side of number line or on right side. Well it is not true. The right infinity ($+$$\infty$) is largest possible value while left infinity ($-\infty$) is smaller than every number except $0.$

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• largest Prime Number :
• The largest prime number discovered so far is $2^{74207281}-1.$
• Professor Curtis Cooper discovered this number. He used 800 university computers to work on this project .
• This number contains over 22 million digits. More precisely $22,338,618$ digits.
• The book on which that number is printed contains three volumes and is available to buy. Good opportunity for book readers.
• This number is 5 million digits longer than previously discovered largest prime number which was also discovered by Professor Curtis Cooper. He held this record four times. yeah! he is Captain Prime.
• The computers took months to check if this number is prime or not. Imagine doing this for countless numbers.
• Isn’t it super cool?

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• Why $0!=1$ & why Factorial of negative number is not defined:
• Let’s take $5!$ for instance. We know that $5!=\frac{6!}{6}=120.$ Let’s write a pattern by following same logic.
• $4!=\frac{5!}{5}=24$
• $3!=\frac{4!}{4}=5$
• $2!=\frac{3!}{3}=2$
• $1!=\frac{2!}{2}=1$
• Now comes $0$
• $0!=\frac{1!}{1}=1$
• Edit : This is not a perfect proof.
• So mystery solved…
• Now get towards negative numbers by following same pattern …
• $-1!=\frac{0!}{0}=\frac{1}{0}=\infty$ (OMG)
• Read next fact to know why $\frac{1}{0}=\infty$

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• Edit : More facts are coming. Let me think for a while…

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Edit : Here comes another one

• Why any number divided by $0$ is $\infty$?
• Let’s take an example of $\frac{16}{4}$ for instance.
• To divide $16$ by $4$, we subtract $4$ from $16$ until we get zero $0.$
• $16-4=12$ , $12-4=8$ , $8-4=4$, $4-4=0$ , We got zero…
• So, the number of times we subtracted 4 from 16 is the answer of $\frac{16}{4}$
• $\therefore \frac{16}{4}=4$ ($\because$ subtraction was 4 times)
• Now do the same for $\frac{25}{5}$ for another example
• Subtract $5$ from $25$ until we get zero
• $25-5=20$ , $20-5=15$ , $15-5=10$ , $10-5=5$ , $5-5=0$
• We did the subtraction five times. So the answer is $\frac{25}{5}=5$
• Now let’s move on with $0$
• Let’s take $20$ and divide it with $0$ by following above method
• Subtract $0$ from $20$ until we get $0$
• $20-0=20$ , $20-0=20,20-0=20,20-0=20,20-0=20,20-0=20,20-0=20,20-0=20,$ whoop
• So, We will get zero $0$ by subtracting $0$ from 20 for infinity times
• Therefor $\frac{20}{0}=\infty$

Now you can look super cool by telling these facts…