= a Googol, which is where Google the corporation got its name.
Googling googol:
A googol can be written in conventional notation as follows:
1 googol = 10100
= 10,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000
A googol is greater than the number of elementary particles in the observable universe.
Avogadro's number, 6.0221415x1023, can loosely be thought of as the number of carbon atoms in twelve grams of elemental carbon, and is perhaps the most widely known large number from chemistry and physics. Avogadro's number is much less than a googol.
Black holes are presumed to evaporate because they faintly give off Hawking radiation; if so, a supermassive black hole would take about a googol years to evaporate.
Seventy factorial, or 70!, is just over a googol, 1.19785717 ? 10100. This means that there are over a googol ways to arrange seventy items (or people) in a sequence (such as a line to a concert).
The Shannon number, 10120, a rough lower bound on the number of possible chess games, is more than a googol.
A googol is considerably less than the number described in the ancient Archimedes' story of The Sand Reckoner, namely But it should be noted that the system invented by Archimedes is reminiscent of a positional numeral system with base 108, so that Archimedes' number could be written , that is, 1 googol in base 108.
In the January 23, 1963 Peanuts strip, Lucy asks Schroeder what the chances are of them getting married, and Schroeder responds "Oh, I'd say about 'googol' to one."
"A googol is precisely as far from infinity as is the number one." ? Carl Sagan, Cosmos
A googolplex is 1 followed by a googol of zeroes, or ten raised to the power of a googol.
In the documentary Cosmos, physicist and broadcast personality Carl Sagan estimated that writing a googolplex in numerals (i.e., "1,000,000,000...") would be physically impossible, since doing so would require more space than the known universe occupies.
Replies
37
Meow
goo goo gah gah! that's alot of number stuff! i just learned that gmail is short for googlemail! 😀
got any pics?
Got it ..... Thanks ;-)
AdminAuthor
The names googol and googolplex were invented by Edward Kasner's nephew, Milton Sirotta, and introduced in Kasner and Newman's 1940 book, Mathematics and the Imagination,in the following passage:
Words of wisdom are spoken by children at least as often as by scientists. The name "googol" was invented by a child (Dr. Kasner's nine-year-old nephew) who was asked to think up a name for a very big number, namely 1 with a hundred zeroes after it. He was very certain that this number was not infinite, and therefore equally certain that it had to have a name. At the same time that he suggested "googol" he gave a name for a still larger number: "Googolplex". A googolplex is much larger than a googol, but is still finite, as the inventor of the name was quick to point out. It was first suggested that a googolplex should be 1, followed by writing zeros until you got tired. This is a description of what would actually happen if one actually tried to write a googolplex, but different people get tired at different times and it would never do to have Carnera a better mathematician than Dr. Einstein, simply because he had more endurance. The googolplex is, then, a specific finite number, with so many zeros after the 1 that the number of zeros is a googol.
Words of wisdom are spoken by children at least as often as by scientists. The name "googol" was invented by a child (Dr. Kasner's nine-year-old nephew) who was asked to think up a name for a very big number, namely 1 with a hundred zeroes after it. He was very certain that this number was not infinite, and therefore equally certain that it had to have a name. At the same time that he suggested "googol" he gave a name for a still larger number: "Googolplex". A googolplex is much larger than a googol, but is still finite, as the inventor of the name was quick to point out. It was first suggested that a googolplex should be 1, followed by writing zeros until you got tired. This is a description of what would actually happen if one actually tried to write a googolplex, but different people get tired at different times and it would never do to have Carnera a better mathematician than Dr. Einstein, simply because he had more endurance. The googolplex is, then, a specific finite number, with so many zeros after the 1 that the number of zeros is a googol.
needs to get out more
ouch, that hurt.
Beach Fanatic
You are really thmart! Now I can sleep well tonight. 😀
Seriously, it is very interesting.
Seriously, it is very interesting.
Beach Fanatic
Tmi
AdminAuthor
Darlene is my middle name, not my nickname
Are you bored? I have a headache...I never was good in math.
Beach Fanatic
Is that a picture of a googol?
hmmmm......can't remember
Is this gonna be on our end-of-the-year test? :blink:
Beach Fanatic
Saying google makes me laugh....😀
Beach Fanatic
Kurt ya have way to much time on your hands!!!!! Go put up some more stickers.:floor::funn::rofl:
Beach Fanatic
Does this come before or after a gazillion?
AdminAuthor
Does this come before or after a gazillion?
It's "gozillion" according to F Gump. :lol:
beats on hood
Kurt is talking about finite numbers, even though they are large. You all need to know that there are much larger numbers.
Aleph-null (
) is by definition the cardinality ("size") of the set of all natural numbers, and (assuming, as usual, the axiom of choice) is the smallest of all infinite cardinalities. A set has cardinality if and only if it is countably infinite, which is the case if and only if it can be put into a direct bijection, or "one-to-one correspondence", with the natural numbers. Such sets include the set of all integers. There are an infinite number of integers, but between any two successive integers there is no other integer.
The cardinality of the set of reals numbers is
. Between any two real numbers are an infinite number of real numbers. It follows from Zermelo-Fraenkel, ZFC, set theory that the celebrated continuim hypothesis, CH, is equivalent to the identity
CH is independent of ZFC: it can be neither proven nor disproven within the context of that axiom system. That it is consistent with ZFC was demonstrated by Kurt G?del in 1940; that it is independent of ZFC was demonstrated by Paul Cohen in 1963.
There are bigger numbers than aleph aero and aleph one -- there's aleph two, etc., etc.
I taught a course on this earlier this year.
Aleph-null (
) is by definition the cardinality ("size") of the set of all natural numbers, and (assuming, as usual, the axiom of choice) is the smallest of all infinite cardinalities. A set has cardinality if and only if it is countably infinite, which is the case if and only if it can be put into a direct bijection, or "one-to-one correspondence", with the natural numbers. Such sets include the set of all integers. There are an infinite number of integers, but between any two successive integers there is no other integer.The cardinality of the set of reals numbers is
. Between any two real numbers are an infinite number of real numbers. It follows from Zermelo-Fraenkel, ZFC, set theory that the celebrated continuim hypothesis, CH, is equivalent to the identity CH is independent of ZFC: it can be neither proven nor disproven within the context of that axiom system. That it is consistent with ZFC was demonstrated by Kurt G?del in 1940; that it is independent of ZFC was demonstrated by Paul Cohen in 1963.There are bigger numbers than aleph aero and aleph one -- there's aleph two, etc., etc.
I taught a course on this earlier this year.
Edited
Meow
Oh my goodness....I would so flunk your course, BR!!! :wave: Those are some fancy symbol thingies you got there!
SoWal Insider
And now a word from the "Real World" of Finance:
Global nominal GDP is $48 Trillion.....
---------------------------------------------
Derivative Trades Jump 27% to Record $681 Trillion
Dec. 10 (Bloomberg) -- Derivatives traded on exchanges surged 27 percent to a record $681 trillion in the third quarter, the biggest increase in three years, the Bank for International Settlements said.
Interest-rate futures, contracts designed to speculate on or hedge against moves in borrowing rates, led the increase with a 31 percent increase to $594 trillion during the three months ended Sept. 30, the Basel, Switzerland-based BIS said today in its quarterly review. The amounts are based on the notional amount underlying the contracts.
Trading surged as investors bet on losses linked to record U.S. mortgage foreclosures and policy changes by the Federal Reserve and the European Central Bank to offset the credit slump. The Fed cut its benchmark interest rate by half a point to 4.75 percent in September, the central bank's first reduction in four years.
``The turbulence in financial markets led to the busiest trading on record,'' BIS analysts Ryan Stever, Christian Upper and Goetz von Peter wrote in the report.
Trading in stock index futures and options rose 19 percent to a record $81 trillion in the third quarter, as investors speculated on whether the credit-market losses would spread to the equity markets.
--------------------------------
:blink: Will we make it to a Quadrillion soon?
.
Global nominal GDP is $48 Trillion.....
---------------------------------------------
Derivative Trades Jump 27% to Record $681 Trillion
Dec. 10 (Bloomberg) -- Derivatives traded on exchanges surged 27 percent to a record $681 trillion in the third quarter, the biggest increase in three years, the Bank for International Settlements said.
Interest-rate futures, contracts designed to speculate on or hedge against moves in borrowing rates, led the increase with a 31 percent increase to $594 trillion during the three months ended Sept. 30, the Basel, Switzerland-based BIS said today in its quarterly review. The amounts are based on the notional amount underlying the contracts.
Trading surged as investors bet on losses linked to record U.S. mortgage foreclosures and policy changes by the Federal Reserve and the European Central Bank to offset the credit slump. The Fed cut its benchmark interest rate by half a point to 4.75 percent in September, the central bank's first reduction in four years.
``The turbulence in financial markets led to the busiest trading on record,'' BIS analysts Ryan Stever, Christian Upper and Goetz von Peter wrote in the report.
Trading in stock index futures and options rose 19 percent to a record $81 trillion in the third quarter, as investors speculated on whether the credit-market losses would spread to the equity markets.
--------------------------------
:blink: Will we make it to a Quadrillion soon?
.
SoWal Expert
:yikes:is all I have to say about that.
AdminAuthor
You all need to know that there are much larger numbers.
:rolling:
beats on hood
:rolling::rolling: to the aleph zero!😀
hmmmm......can't remember
Here's my four ha'pennies :blink: (or 2/25ths of 2 bits?):
I have long held the theory that there are only 200 people in the world because I can only comprehend 200 people at one time. (I made this up in the early '90s, and Jimmy Buffett didn't write about it until a few years ago, for those of you who keep up with this sort of thing.)
When you're talking about gazillions and googols, those are not numbers. They are bunches. I can comprehend 200 bunches of numbers, and the bunches can be as big as you want as long as they stay in bunches.
Kurt and BR, you're talkin' crazy talk. Let me know when you want to discuss something between 1 and 199...
I have long held the theory that there are only 200 people in the world because I can only comprehend 200 people at one time. (I made this up in the early '90s, and Jimmy Buffett didn't write about it until a few years ago, for those of you who keep up with this sort of thing.)
When you're talking about gazillions and googols, those are not numbers. They are bunches. I can comprehend 200 bunches of numbers, and the bunches can be as big as you want as long as they stay in bunches.
Kurt and BR, you're talkin' crazy talk. Let me know when you want to discuss something between 1 and 199...
SoWal Expert
Here's my four ha'pennies :blink: (or 2/25ths of 2 bits?):
I have long held the theory that there are only 200 people in the world because I can only comprehend 200 people at one time. (I made this up in the early '90s, and Jimmy Buffett didn't write about it until a few years ago, for those of you who keep up with this sort of thing.)
When you're talking about gazillions and googols, those are not numbers. They are bunches. I can comprehend 200 bunches of numbers, and the bunches can be as big as you want as long as they stay in bunches.
Kurt and BR, you're talkin' crazy talk. Let me know when you want to discuss something between 1 and 199...
Thank you.
hmmmm......can't remember
Thank you.Anytime, darlin'. I'm not skeered to admit my limitations! 😀
Meow
Thank you.
:clap:...to the aleph zero!
AdminAuthor
To infinity and beyond!
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