Mathmatical tricks

Numbers one to nine are single digits and follow a precise numerical order repetitive sequence. After nine they reset to one zero making ten a double digit one zero number. At this point the one to nine repeat again in this case one zero, one one, one two, one three, one four, one five, one six, one seven, one eight and one nine respectively.

Our mathematical instinct agrees they repeat two zero, two one, two two, two three, two four, two five......to two nine followed again by three zero, three one, three two, three three, three four, three five.........repeating the zero to nine single digit numbers from three nine, four zero, four one, four two, four three, four four, four five............and so four nine, five zero, five one, five two, five three, five four, five five........ five nine, six zero........and so on.

Our instinct in such matters agrees single zero to nine numbers repeat in the sixes, sevens, eights, nines to nine nine before resetting to one zero zero.

After nine nine nine is one, zero zero, for a hundred followed by one, zero one, one, zero two, one zero three, one, zero four, one zero five in numerical order like that to nine nine nine resetting to one zero zero zero. Our instinct in these matters won't argue a four digit number for a thousand because we are including the one.

They continue to nine nine nine nine resetting to one zero zero zero zero for ten thousand followed by one zero zero zero one to nine nine nine nine nine resetting to one zero zero zero zero zero followed by one zero zero zero zero one constantly repeating in numerical the same zero to nine single digits like that.

The important point a zero makes one into a two digit number for ten our mathematical instinct won't argue with that. Another zero is a three digit number for a hundred and another zero makes it a four digit number for a thousand and another zero makes the one a five digit number for ten thousand respectively. Each zero represents a ten times progression of the zero to nine linear counting expressed as none linear or logarithmic positive numbers.

Anybody observant would have noticed one, ten, a hundred, a thousand, ten thousand a hundred thousand and million paten. There is a no zeros for one, one zero for ten, two zeros for a hundred, three zeros for a thousand, four zeros for ten thousand, five zeros for a hundred thousand and six zeros for a million respectively. Adding a zero makes the previous ten times greater.

By now your mathematical instinct will agree it noticed adding a zero was one multiplied by ten. Your math's skill tells you it agrees adding another zero constitutes to ten multiplied by ten giving us a hundred. You math's instinct agrees adding another zero gives us a hundred multiplied by ten giving us a thousand. It agrees if we add another zero gives us thousand multiplied by ten and another zero added giving us ten thousand multiplied by ten respectively. Your instinct agrees with the statement every zero added is multiplied by ten times.

It agrees adding another zero gives us ten million, adding anther zero gives us another ten times, a hundred million and adding another zero gives us another ten times and another zero gives us another ten times. Your math's instinct agrees is equal to one multiplied by ten twelve times giving you a thirteen digit number ( one and twelve zeros )  for a billion and so on.

And so your instinct agrees if we add another zero becomes ten times for ten billion, another zero makes it a hundred billion and another zero makes it a thousand billion respectively. Your instinct can tell by adding zeros counts ten times greater than the every previous. Your instinct tells you we can count well into excess of multiplying one by ten billions and billions of times over with out end and agrees with the statement no where near infinity. It agrees with the statement if we multiply one by ten a billion times gives us a billion zero long number and we can add any number of more zeros and still never reach infinite agreeing because adding zeros can have no end.

Operating on the principle we can take an acceleration of a meter per second as every ten times the distance. If we do the arithmetic on this we would accelerate from zero movement to a meter by the end of a second. By the end of the second second we'd accelerated ten meters. By the end of the third second a hundred meters, and by the end of the fourth second a thousand meters. Our mathematical instinct agrees the standard metric system tells us there is a thousand meters in a kilometer, therefore won't argue we traveled a kilometer by the end of four seconds.

Our math's instinct agrees by the end of five seconds we'd  traveled ten kilometers. It won't argue by six seconds we accelerated a hundred kilometers. By seven seconds we accelerated distance of a thousand kilometers. By eight seconds. ten thousand. By nine seconds a hundred thousand. By ten seconds a thousand thousand kilometers.

Our instinct agrees if we keep accelerating like that we reach beyond the limits of our solar system less than quarter minute. ( fifteen seconds ). If we keep accelerating ten times the distance every second we would have accelerated way-way beyond the distance light travels a second in less than a quitter minute ( thirty seconds ). You insect agrees with the statement because we are accelerating all the time. It will agree we would be some hundreds and thousands of billons of kilometers across the universe in less than three quarter minute ( Forty five seconds ) Anybody curious enough and into challenging math's will be able to figure out how far we would travel in a full minute at tems times the distance every second.

Light travels a distance of just under three hundred thousand kilometers ( or a hundred and eighty six thousand miles if you like ) in a second. If we keep accelerating ten times the distance every second like that we would reach a point of trillions upon trillions trillions of kilometers across the universe in less than quarter hour. Imagine the distance in an exact hour, let a lone in an exact  day, a week, a month or a year. Imagine in a decade, a century, a millennia ( ten times the distance every second in a thousand years ) a million or a billion or even in a trillion centuries.

The numbers can go the opposite direction expressed as negative. Water is a good example. It freezes solid at zero degrees Celsius. This is the point where it cannot freeze any further despite getting colder and colder bellow the zero point past zero degrees cold.

A degree bellow zero is minus one, two degrees bellow zero is minus two and so on where it can get as cold as minis two hundred and seventy three degrees bellow zero where it is the point all activity of the atom in matter ceases. People feel hardship at minus ten degrees bellow zero. They will only last less than quarter minute exposed to minus thirty degrees. Instant death at flirty degrees. When atoms cease activity coldness can't go any further than two hundred and seventy three. It is believed this is the level of coldness deep inside black holes or at lest one or two degrees above. Such as minus.

Minus is summed up as reciprocals of the positive numbers. One degree above zero is the reciprocal of one degree above zero. So too ten degrees above zero is the reciprocal of the same number bellow one respectively. If we take for argument sake ten we can relocate the zero to the left of one between a full stop is minus ten of the same number of plus ten. In other words the reciprocal of ten is is one divided by ten, So the reciprocal of ten is a tenth expressed as zero point one and the reciprocal of a tenth is ten. In other words a reciprocal of each other.

The reciprocal of a hundred is one divided twice by ten or equal to one divide a hundred giving zero point zero one or a hundredth. Zero point zero, zero one is a the reciprocal of a thousand because it is one divided by a thousand or one by ten three times. In other words a minus of the same positive number the zeros on the left of the one. In other words thousandth is zero point zero, zero, one and the reciprocal of the same number of zeros on the right of one, and the reciprocal of a million is the same six zeros on the left of one.

In other words the reciprocal of ten is zero point one, the reciprocal of a hundred is zero point zero one, the reciprocal for a thousand is zero, point, zero, zero, one and so on. Both the positive and minus numbers are the same number. We can say the reciprocal of one is the reciprocal of ten as tenth is the reciprocal of a tenth as a hundred is the reciprocal of a hundredth and the reciprocal of a thousand is a thousandth and so on. It is clear in the paten they are reciprocals of each other. The minus of the positive and the positive of the minus respectively. A millionth and a million are the same number only reciprocals of each other.

Our mathematical instinct agrees a ten tenth's is equal to a whole one just as a million millionth's equals a whole one respectively.

Operating on the principle of one multiplied by ten many times we can dived one by ten cording to a number times. Our mathematical instinct away recognizes immediately the reciprocal of a trillion is a trillionth and a trillionth trillionth's equals a one. We see straight away infinity says just as we can add zeros to positive numbers indefinitely. we can add and add the minus zeros indefinably. A billon zero number is the reciprocals of the same number of zeros in the minus scale.

Scientific notation for such large numbers is called ten to the........ in the positives and ten to the minus in the minuses. Ten to the.......is a little razed number of time to be multiplied by just to the right of ten times any number you like the first two digits with full stop called a point. For example three thousand five hundred and seventy is notated to three point five seven times ten to the three. Proof when you multiply three point five seven by ten three times.

An identical procedure for minuses. For example three point five seven times ten to the minus three gives you zero zero zero three five seven the reciprocal of three thousand five hundred and seventy respectively. The only difference is the little take away sign just to the right between ten to the three multiplier.

Our mathematical instinct  recognizes immediately some numbers always divide with fractions over and yet others dived evenly. Mathematicians  calls any number that divides with fractions over a prime. Including one, these numbers happen to be two, three, five seven and nine. That leaves the rest of the single digit numbers, four, six, and eight that divide with no fractions mathematicians called composites. We can see clearly in the answer columns of children's time tables they are all exclusively composite numbers.

The arithmetic has intrigued mathematicians for centuries. If we take zero asking ourselves how many go into itself since zero is nothing anyway is represented by the number zero. So we can say zero divided by zero is zero

In digital electronics a brief surge of current is the number one. A good example is a keyboard keystroke, touch screen or mouse movement and clicks clicks. When there is no signal means the number zero. Zero and one are called bits and as they are a pair is expressed as binary meaning pair.

In binary arithmetic dividing one by one is an arithmetic signal to reset the one back to zero. In other words a touch screen a signal is on when we move the screen and when we don't is no signal. The arithmetic sets zero to a one reset back to zero in a endless resetting of zero and one sequences. In other words zero plus zero is a signal to change the zero to one. The same is true for zero times zero, zero dived zero, or zero takeaway zero constantly resetting zero back to one and the one back to zero.

Eight bits is called a byte meaning there is two hundred and fifty six possible combinations. Our mathematical instinct recognizes straight away  doubling eight bits is multiplied by two is sixteen bites. The total combination of sixteen bites becomes two hundred and fifty six of the eight bits multiplied by itself. Any number multiplied by itself is called a square. Once we learn eight bits doubled the total combination is squared we recognize instinctively doubling every byte constitutes a total of the zero and one bits combination is squared.

We won't have any argument from our math's instinct eight bits doubled equals the combination squared for sixteen bits, sixteen bits doubled a binary combination for thirty two bits and a binary combination for thirty two bits squared equals the total combination of sixty two bits and and so on.

Mathematicians have been intrigued with the number one for centuries. It is because it divides into all numbers both composite and primes. We can see this when ask our mathematical instinct how many ones go one. The instinct knows of course it is only one one. How about the same question into a prime such as three? Our math's instinct tells us of course there are three ones in three.  Over the centuries mathematicians have been intrigued under certain circumstances zero and one work out as primes and other circumstances don't.

The same is true with any composite. Our instinct knows by asking ourselves how many ones go into four. Of course there are four ones in four. We can apply our keen instinct by asking how many fours go into four.  Obviously one four. The same is true with the rest of the composites. Thus one goes evenly in both prime and composites. Our instinct agrees with the statement arithmetic doesn't lie you know. Obviously not just for primes but all numbers that's including all the composites we observe in the answer columns in children's time tables.

We can apply our mathematical instinct asking ourselves what is half of four. Our instinct says of course we get two. It tells us because obviously two two's are four. However if we ask the same question with a prime like five we have a fraction over. The same is true of all primes. If we take a composite like ten we can ask how many, two's ( a prime ) go into it. Our arithmetic instinct tells us because five ( a prime ) two's ( the secondary prime ) are ten because obviously two fives is ten. We can't do this with primes. You can check the arithmetic composites in  the children's times table chart.

If we take the composite number ten from a times ten table dived in half is dividing by two discovering two is a prime. We discover though we can dived two in half that is one. Our mathematical instinct  notices as far as we can dived the composite evenly. The same rule applies to any and all of the rest of the sums in the entire tables. Other wise always a fraction over. If we take three seven's are twenty one ( a composite ) three and seven are the prime factors that add up to the composite. This is true for every sun in the children's time tables. To prove this check out three three's are nine. Nine is a composite because it can be divided by another prime ( three ) with out a fraction over.

Playing round with the children's time table charts we discover we cannot dived evenly any further because we had found prime factors involved in the sum. The children's times table is a double composite number sequences. Take the times two table. In numerical order sequence in the answer column, two zeros are two. two ones are two, two three's are six, two four's are eight, two fives are ten and so on. The same is true with every table. In other words we are adding every two step. We can clearly see this with the rest of the times table.

When we check out times three we can clearly see every step is an addition of threes. We can see this paten when we check out any table such as times seven there is a addition of sevens every step.

If we try the same with three digit composites the arithmetic rules apply. We will discover applied to four digit numbers works just as well. We can apply to five, six, seven, eight, nine, ten, eleven.......digit long numbers and we find the prime factors. The only difficulty is such big numbers. There is no limit to the number of digits in a number twenty five, thirty, fifty, a hundred, thousands ten thousand digit numbers even trillion digit long number.