Skip to main content

Mathematics for Computer Scientists | Integers


Numbers

Defendit numerus: There is safety in numbers

We begin by talking about numbers. This may seen rather elementary but is does
set the scene and introduce a lot of notation. In addition much of what follows is
important in computing.

Integers

I will assume you are familiar with the integers.
1,2,3,4,. . .,101,102, . . . , n, . . . , 2^32582657 − 1, . . .
sometime called the whole numbers. These are just the numbers we use for count-
ing. To these integers we add the zero, 0, defined as:
0 + any integer n = 0 + n = n + 0 = n
Once we have the integers and zero mathematicians create negative integers by
defining (−n) as:
the number which when added to n gives zero, so n + (−n) = (−n) + n = 0.
Eventually we get fed up with writing n+(−n) = 0 and write this as n−n = 0.
We have now got the positive and negative integers {. . . , −3, −2, −1, 0, 1, 2, 3, 4, . . .}
You are probably used to arithmetic with integers which follows simple rules.
To be on the safe side we itemize them, so for integers a and b

1.  a + b = b + a
2.  a × b = b × a or ab = ba
3.  −a × b = −ab
4.  (−a) × (−b) = ab
5.  To save space we write a k as a shorthand for a multiplied by itself k times.
So 3^4 = 3 × 3 × 3 × 3 and 2^10 = 1024. Note a^n × a^m = a^(n+m)
6.  Do note that n^0 =1.

Peace Out
@suhaibbinyounis

Comments

Popular posts from this blog

Make money with Quora Partner Program | Explained

Earning money ain't it...
I know we all have some time wondered if it is possible to earn money online and believe me there are many ways to do that and it is all amazing.
In this post I will specifically talk about Quora Partner Program, QPP.

Quora came out with this amazing program that allows anyone in world to make a living out of writing. But speaking the truth it is not that much. It quite a hard work and less pay job.
Bascially, all you do is ask questions and then these questions will receive Ad impressions for which you get paid.

But here is the deal, you can monetize a question only for 1 year only. After that Quora owns the question.


So, how do you get started?

As of now there is no direct way of joining the QPP. The only way for you to join is if you receive a email from Quora itself which is quite random and obviously how active you are on quora will play a part.


So, how much can i earn?
Well, there is no limit on how much you can earn. Generally the money is way too low but t…

RESOLVING NETWORK ISSUES ON LINUX | LINUX SERIES

Dealing with networking issues can be a very challenging task. A packet sent from a client to a server (or vice versa) might be dropped in various locations and for various reasons. Some of the most common cases are -
1. A firewall that is blocking the packet. It can be a firewall on the server side, on the client side or any firewall along the way between the server and the client. The blocking may be based on an ip (source and/or destination), ports (in case of tcp/udp) or any other layer 3,4 criteria.

2. Lack of layer 2 connectivity.

3. Routing configurations that are not set properly.

Fortunately, Linux command line tools supply significant information that might help us narrow down the problem. From my experience those are my top 8 tools that will help you overcome networking issues.
 ping
This is the most fundamental command when troubleshooting a networking issue. The ping command will test the network connectivity between your host and the server. This is definitely the first comman…

Magic SysRq key | Linux Rescue | Frozen Linux | LINUX SERIES

The magic SysRq key is a key combination which allows the user to perform various low-level commands regardless of the system's state. If your Linux machine freezes or you want to reboot your Linux machine without corrupting the filesystem you can use this magic SysRq key combination. This key combination provides access to powerful features and thus needs some knowledge to use it. Please do not proceed without knowing about these combinations as you may put your system in a critical state. Please note that this magic SysRq key cannot work under certain conditions, such as a kernel panic or a hardware failure preventing the kernel from running properly.
Commads:The key combination consists of Alt+SysRq and another key, which controls the command issued. SysRq may be released before pressing the command key, as long as Alt remains held down.
These combinations always assume the QWERTY keyboard layout.
1. Immediately reboot the system, without unmounting or syncing filesystems - b 2. Perfor…