History[ edit ] In BC, Plato 's Parmenides may have contained an early example of an implicit inductive proof.

The basis of computing You may be wondering how a simple number is the basis of all the amazing things a computer can do. Believe it or not, it is! The processor in your computer has a complex but ultimately limited set of instructions it can perform on values such as addition, multiplication, etc.

Essentially, each of these instructions is assigned a number so that an entire program add this to that, multiply by that, divide by this and so on can be represented by a just a stream of numbers.

For example, if the processor knows operation 2 is addition, then could mean "add 5 and 2 and store the output somewhere". In the days of punch-cards, one could see with their eye the one's and zero's that make up the program stream by looking at the holes present on the card.

Of course this moved to being stored via the polarity of small magnetic particles rather quickly tapes, disks and onto the point today that we can carry unimaginable amounts of data in our pocket.

Translating these numbers to something useful to humans is what makes a computer so useful. For example, screens are made up of millions of discrete pixels, each too small for the human eye to distinguish but combining to make a complete image.

Generally each pixel has a certain red, green and blue component that makes up it's display color. Of course, these values can be represented by numbers, which of course can be represented by binary! Thus any image can be broken up into millions of individual dots, each dot represented by a tuple of three values representing the red, green and blue values for the pixel.

Thus given a long string of such numbers, formatted correctly, the video hardware in your computer can convert those numbers to electrical signals to turn on and off individual pixels and hence display an image.

As you read on, we will build up the entire modern computing environment from this basic building block; from the bottom-up if you will! Bits and Bytes As discussed above, we can essentially choose to represent anything by a number, which can be converted to binary and operated on by the computer.

For example, to represent all the letters of the alphabet we would need at least enough different combinations to represent all the lower case letters, the upper case letters, numbers and punctuation, plus a few extras. Adding this up means we need probably around 80 different combinations.

If we have two bits, we can represent four possible unique combinations 00 01 10 If we have three bits, we can represent 8 different combinations.

In general, with n bits we can represent 2n unique combinations. We call a group of 8 bits a byte. Guess how big a C char variable is? ASCII Given that a byte can represent any of the values 0 throughanyone could arbitrarily make up a mapping between characters and numbers.

For example, a video card manufacturer could decide that 1 represents A, so when value 1 is sent to the video card it displays a capital 'A' on the screen. A printer manufacturer might decide for some obscure reason that 1 represented a lower-case 'z', meaning that complex conversions would be required to display and print the same thing.

This is a 7-bit code, meaning there are 27 or available codes. The range of codes is divided up into two major parts; the non-printable and the printable. Printable characters are things like characters upper and lower casenumbers and punctuation.

Non-printable codes are for control, and do things like make a carriage-return, ring the terminal bell or the special NULL code which represents nothing at all. To alleviate this, modern systems are moving away from ASCII to Unicode, which can use up to 4 bytes to represent a character, giving much more room!

This can be used to implement parity which is a simple form of error checking. Consider a computer using punch-cards for input, where a hole represents 1 and no hole represents 0.

Any inadvertent covering of a hole will cause an incorrect value to be read, causing undefined behaviour. Parity allows a simple check of the bits of a byte to ensure they were read correctly. We can implement either odd or even parity by using the extra bit as a parity bit. In odd parity, if the number of 1's in the 7 bits of information is odd, the parity bit is set, otherwise it is not set.

Even parity is the opposite; if the number of 1's is even the parity bit is set to 1. In this way, the flipping of one bit will case a parity error, which can be detected.

XXX more about error correcting 16, 32 and 64 bit computers Numbers do not fit into bytes; hopefully your bank balance in dollars will need more range than can fit into one byte! Modern architectures are at least 32 bit computers.

This means they work with 4 bytes at a time when processing and reading or writing to memory. We refer to 4 bytes as a word; this is analogous to language where letters bits make up words in a sentence, except in computing every word has the same size! The size of a C int variable is 32 bits.

Modern architectures are 64 bits, which doubles the size the processor works with to 8 bytes. Kilo, Mega and Giga Bytes Computers deal with a lot of bytes; that's what makes them so powerful!Write a set representing all even natural numbers less than 9 (use commas to separate answers.

Type the number - Answered by a verified Math Tutor or Teacher Math questions. Write a set representing all even natural numbers less than 9 (use commas to separate answers.

Type the number in ascending order) 2. True or False. 11 = {} 3. All rational numbers are "canonicalized" as they're read--that's why 10 and 20/2 are both read as the same number, as are 3/4 and 6/8.

Rationals are printed in "reduced" form--integer values are printed in integer syntax and ratios with the numerator and denominator reduced to lowest terms. (i) The set of odd numbers less than 7 is written as: {odd numbers less than 7}.

(ii) A set of football players with ages between 22 years to 30 years. (iii) A set of numbers greater than 30 and smaller than . MAT Ch02 Terms/Formulas/Q's study guide by tammy_hobbs includes 41 questions covering vocabulary, terms and more.

Write a set representing all odd natural numbers less than 9. The set of all odd natural numbers less than 9 is? The set of even counting numbers less than 10 *Listing method {2, 4, 6, 8}.

Jun 12, · (b) B= the set of even numbers between 1 and 9= {even numbers between 1 and 9}= {2,4,6,8} The curly brackets or braces {} means ‘the set of’.

(c) the vowels in the english alphabet (d) even numbers less than Not sure about the even/odd numbers, because in base 10, Both “14” and “24” are even, and have a different number of even digits (I might be misinterpreting the meaning of your questions.) In an odd-number base system (like base 3) it becomes more tricky to tell when a number is even.

- The importance of intervention health program for students
- Mental model mindsets paper essay
- Effects of change on nursing practice
- Child observation paper
- Toefl essay music
- Business plan canvas osterwalder kpp
- The unfranchise business presentation
- Automotive business plan ppt outline
- Global brand management
- The treaty of versailles the treaty of neuilly and the treaty of saint germaine were ineffective in

TYPES OF NUMBERS: a glossary