Anees Rao 6.999... is perfectly equal to 7. There have been some posts about that in this community not so long ago. An easy way to seeing it is 6.999... = 6 + 0.999... = 6 + 3*0.333... = 6 + 3*1/3 = 6 + 1 = 7
You could also use limits when you want to be more strict, the equation I gave is more to give you an idea of what is going on.
The decimal representation of a number is not unique!
To me, "g" has nothing to do on this clock ... but it is not because the value sould be wrong. Its just that all the ways the numbers are written refer to MATH convepts, terminology and/or number properties ... while g is a PHYSICAL constant of nature !! So, for g the result depends in more of a defintion of what it means physically, of a choice of units .. while none of the others do: they depend only of the defintions of what is written. In MKS standard system of unit, of course what is written values 10 .. But in CGS system the value is 982 !!!
Praveen Kumar 0.999bar = 0.9 + 0.09 + 0.009 +... an infinite geometric series with r=0.1 the sum is then given by 0.999bar = a_1 / (1 - r) = 0.9 / (1 - 0.1) = 1
"Infinite series" is a contradiction in terms, despite the fact that the phrase is used colloquially, even by mathematicians, to refer to non-terminating sequences of partial sums. Infinite is not the same as non-terminating. Infinite is a false concept; non-terminating is a perfectly reasonable idea.
To be precise and correct:
For any given real z>0, there exists positive integer n such that the difference between 1 and the Nth partial sum of the sequence generated by the formula
Ceiling function of the gravitational constant does belong on this analog watch, if u don't agree is cos u have no clue why belongs there....this is an ANALOG WATCH.
I got it the (tan) 45 = 1 .......so its placed where the number one would be as to say one o'clock. ...subsequently square of 4 = 2 and is where the 2 should be.....yea nice nice I want a clock as this one....THIS IS GREAT NOT ART ..ITS EDUCATIVE GREAT ART
the g here is the gravitational acceleration whch is by standard 9.8 the square brackets around it signify the greatest integer or the ceiling function....so we gt a 10 ...
Nice :)
ReplyDeletethat 's sooo cool !!!!
ReplyDeleteCan you explain 11 please?
ReplyDeleteThink base 16...
ReplyDeleteAh... OK.. It's 0x0b.... Thx
ReplyDeletedont know no 10, 11, and 12 ...
ReplyDelete10 = ceiling function of the gravitational constant
ReplyDelete11 - 0b in hex notation
12 - 1100 in binary notation
Very intrestiiiiiiin
ReplyDeleteoh..thank you! Himanshu Ghadigaonkar Kimo Salen
ReplyDeleteI think I never learn hex notation and binary notation in school...have to google it..hee:)
ahhh lets buy a digital watch now
ReplyDelete6.9999999(etc) is 7? Not really no? Everything else is perfect though.
ReplyDeleteThat's not g. the brackets indicate ceiling of the number. then again, g is only a local constant no? that's not acceptable too. point accepted!
ReplyDeleteAnees Rao why is it not acceptable? the ceiling function is a number operator so it's valid to use on any constant.
ReplyDeleteand 0.999(non-terminating) is equal to 1.
I want one for my computer room.....
ReplyDeleteAnees Rao 6.999... is perfectly equal to 7. There have been some posts about that in this community not so long ago.
ReplyDeleteAn easy way to seeing it is 6.999... = 6 + 0.999... = 6 + 3*0.333... = 6 + 3*1/3 = 6 + 1 = 7
You could also use limits when you want to be more strict, the equation I gave is more to give you an idea of what is going on.
The decimal representation of a number is not unique!
Sleeping Menace I think this would be good for the spa I go to....ummmm more massage time for me :))))))
ReplyDeleteable to understand all others except 6.9bar. I would be grateful if someone cleared my doubt...
ReplyDeletegood way of thingking
ReplyDeleteTo me, "g" has nothing to do on this clock ...
ReplyDeletebut it is not because the value sould be wrong.
Its just that all the ways the numbers are written refer to MATH convepts, terminology and/or number properties ...
while g is a PHYSICAL constant of nature !!
So, for g the result depends in more of a defintion of what it means physically, of a choice of units .. while none of the others do: they depend only of the defintions of what is written.
In MKS standard system of unit, of course what is written values 10 .. But in CGS system the value is 982 !!!
Corina Marinescu hmmm.. massage...that would break up the day nicely were it only an option... :)
ReplyDeleteBut I like natural numbers! :(
ReplyDeleteThis will definitely help a lot! :)
ReplyDeleteWay cool..
ReplyDeleteDavid Chako Natural numbers are boring ;)
ReplyDeleteNatural numbers = Rodney Dangerfield
ReplyDeletePraveen Kumar 0.999bar = 0.9 + 0.09 + 0.009 +...
ReplyDeletean infinite geometric series with r=0.1
the sum is then given by
0.999bar = a_1 / (1 - r) = 0.9 / (1 - 0.1) = 1
so 6.999bar = 6 + 0.999bar = 6 + 1 = 7
"Infinite series" is a contradiction in terms, despite the fact that the phrase is used colloquially, even by mathematicians, to refer to non-terminating sequences of partial sums. Infinite is not the same as non-terminating. Infinite is a false concept; non-terminating is a perfectly reasonable idea.
ReplyDeleteTo be precise and correct:
For any given real z>0, there exists positive integer n such that the difference between 1 and the Nth partial sum of the sequence generated by the formula
0.9*pow(10,-n)
for n=0,1,2,3,...
is less than z.
Which is to say, 0.9bar is equivalent to 1 in the metric space of real numbers.
ReplyDeletetoo much!!
ReplyDeleteIt's 69 timeeeeeeeee
ReplyDeleteWith ubiquitous digital clocks many kids have trouble with analog time displays, this would just drive them crazy. Boy would I love one of these.
ReplyDeleteabsolutelly cool :-)
ReplyDeleteI wonder if I can get this in South Africa
ReplyDeletewhere I can get one?
ReplyDeletenerd clock
ReplyDelete1100 in binary is 12 . It threw me off for a second.
ReplyDeletewhere i can get one?
ReplyDeleteI agree that g does not belong.
ReplyDeleteCeiling function of the gravitational constant does belong on this analog watch, if u don't agree is cos u have no clue why belongs there....this is an ANALOG WATCH.
ReplyDeleteI wanna one of this.....:)
ReplyDeleteI want THIS :)
ReplyDeleteWhere can I get this? For my chemistry class
ReplyDeleteOh well nice
ReplyDeleteI got it the (tan) 45 = 1 .......so its placed where the number one would be as to say one o'clock. ...subsequently square of 4 = 2 and is where the 2 should be.....yea nice nice I want a clock as this one....THIS IS GREAT NOT ART ..ITS EDUCATIVE GREAT ART
ReplyDeletethe g here is the gravitational acceleration whch is by standard 9.8 the square brackets around it signify the greatest integer or the ceiling function....so we gt a 10 ...
ReplyDelete