Freethought & Rationalism Archive

irichc · 01-13-2003, 08:39 AM

Quote:

Originally posted by Biff the unclean
No one called you a "rat" Daniel.
"I smell a rat" is an expression in English which means "I sense something is amiss," or "I think someone is tricking me."

I apologize. You were misunderstood.

Daniel.

Biff the unclean · 01-13-2003, 08:42 AM

Einstein was some kind of pantheist.

Einstein wasn't a theist at all, and was quite outspoken about it at Princeton. The famous pantheistic quotes of his were actually the idea of his wife. She was concerned about Albert's public relations, he being a celebrity and McCarthy being in Washington.

Biff the unclean · 01-13-2003, 08:55 AM

...if the atheist is right, he will never realize it.
Daniel, once again you are offering information about God. This time it's about God's personal preferences and his future plans for Atheists.
If you are unable to show proof that there even is such a thing as a God where are you getting this very specific information from? And how do you know that it is true?

Hawkingfan · 01-13-2003, 09:00 AM

Quote:

Originally posted by irichc
Too late to get salvation, a life passed in vain.

Daniel.

Don't be so sure. You may be in as just as much trouble as an atheist, Daniel. Please consider what a Muslim once posted as feedback to the Secular Web:

The Koran was revealed from ALLAH this is why so many scientific facts are contained in it's text.

Christians who worship Jesus as God (which is the vast majority of Christians) will be sent to Hell. The question is why are all these people sent to Hell?

"And whoever seeks a religion other than Islam, it will never be accepted of him, and in the afterlife he will be among the lost." (Surat Aal Imraan 3:85)

"Those who reject faith and deny our signs will be companions of Hell-fire." (Al-maidah 5:10)

"They take their priests and their anchorites to be their lords in derogation of ALLAH, and (they take as their Lord) christ, the son of mary; yet they were commanded to worship but one god: there is no god but one god: there is no god but he. Praise and glory to Him: (far is he) from having the partners they associate(with him). (At-Touba 9:31)

They will go to hell for making false statements about ALLAH and disobeying the creator. Disbelief, associating partners, sons, gods...etc. with ALLAH is why most men\women will go to HELL.

As the Koran states; "Those who reject our signs,we shall soon cast into the fire; as often as their skins are roasted through, we shall change them for fresh skins, that they may taste the penalty: for ALLAH is exalted in power, wise." (al-nisaa 4:56)

[If one's skin was changed over after being burnt, there would be no way to become used to the flames.]

PLEASE READ THE Koran AND BY ALLAH'S WILL BECOME ONE OF THE GUIDED.

Hawkingfan · 01-13-2003, 09:28 AM

originally posted by irichc : "can you prove to me you can count infinite?"

Anyone can count a large number or up to a large number, no matter how large it is. But the problem is trying to stop at the end. So I think the problem you may be referring to is "Can you count and reach the end of all numbers?" which the obvious answer is "no" because numbers go on forever.

originally posted by irichc: "Can any mathematician picture infinity?"

Yes! Calculus has an uncanny way of explaining things that would otherwise be very difficult to understand. The hard-to-grasp concept of infinity is one of these specialties that Calculus (specifically Differential and Integral) is irreplaceable in explaining.

Many things increase at different rates (sometimes constantly and without end, like infinity) which can be described by Functions. Many of Calculus's functions have Limits (a very important part of Calculus) that surpass boundaries beyond logic! This means that the domains and ranges cannot be contained in numbers that we can work with, because the numbers keep getting larger (they do not stop, like infinity). But this functional problem is easily taken care of by the use of infinite limits (divergence), even though the limits cannot exist AT infinity. Yet each of these functions of growth has some factor that allows it to grow only so much.

These concepts can be drawn on a graph. Graphically speaking, limits involving infinity result from functions that have horizontal, and/or vertical, asymptotes. An asymptote is a value in the domain or range that the function is not defined at (most often to avoid division by zero). Horizontal asymptotes occur at restricted y - values, and vertical asymptotes occur at restricted x- values. This creates a graph that approaches these asymptotes but never actually touches them.

As the values of x approach vertical asymptote(s) the values of y tend toward +/- infinity. When a function has horizontal asymptote(s) the y � values approach the asymptote as the x � value approach +/� infinity.

The properties for limits as x---> +/� infinity can be applied to higher order polynomials, and rational functions. If a rational function can be reduced, then the properties may be applied to it in order to find the limit.

The function is reduced by dividing each element by the highest power of x in the denominator. The reason for this is to create a function that contains a constant and multiples of 1/x in the denominator. Once the function is of this form we know the limits of each term and may apply the properties of limits.

An infinite limit describes the limit of a function that keeps growing as x approaches a given value.
The two main occurrences of infinite limits are:
1) The limit as x approaches the value of a vertical asymptote, the value of the function is always growing.
2) Any polynomial of degree 1 or greater. (This includes simple functions of the form f(x) NOT rational functions of the form f(x)/g(x)). These polynomials will eventually take off to infinity. Which gives them a limit of +/-infinity as x---> +/-infinity.

What happens when the degree of the numerator exceeds the degree of the denominator is that the limit goes to infinity.

To find the limit as x---> +/-infinity of a rational function compare the degree of the numerator and denominator:
a) same degree: the limit equals the ratio of the coefficients of the highest order terms.
b) numerator of lower degree: the limit equals 0, because all of the terms in the numerator will be multiples of 1/x, and the limit of the numerator will be 0.
c) numerator of higher degree: the limit will approach +/-infinity. The direction of the limit will depend on the interaction of the signs in the numerator and denominator as x---> +/-infinity.
When we deal with the limits of quantities, very often we have to compare numbers such as:

adding two large numbers (they can be infinite);

multiplying two large numbers;

subtracting two large numbers;

multiplying a large number with a small number;

Though it is easy to check that adding two large numbers is a large number (that is infinity+infinity=infinity), it is absolutely not clear what happened if we subtract a large number from another large number. We say that we have an indeterminate form. May be one of the most important indeterminate form is the quotient of two small (or large) numbers.

Infinite Limits for Rational Functions, Divergence, Vector Spaces, Infinite Intervals...these only scratch the surface of what Calculus can do.

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01-13-2003, 08:42 AM	#72
Biff the unclean Banned Join Date: Oct 2002 Location: an inaccessible island fortress Posts: 10,638	Einstein was some kind of pantheist. Einstein wasn't a theist at all, and was quite outspoken about it at Princeton. The famous pantheistic quotes of his were actually the idea of his wife. She was concerned about Albert's public relations, he being a celebrity and McCarthy being in Washington.

01-13-2003, 08:55 AM	#73
Biff the unclean Banned Join Date: Oct 2002 Location: an inaccessible island fortress Posts: 10,638	...if the atheist is right, he will never realize it. Daniel, once again you are offering information about God. This time it's about God's personal preferences and his future plans for Atheists. If you are unable to show proof that there even is such a thing as a God where are you getting this very specific information from? And how do you know that it is true?

01-13-2003, 09:28 AM	#75
Hawkingfan Veteran Member Join Date: Oct 2002 Location: Texas Posts: 1,247	originally posted by irichc : "can you prove to me you can count infinite?" Anyone can count a large number or up to a large number, no matter how large it is. But the problem is trying to stop at the end. So I think the problem you may be referring to is "Can you count and reach the end of all numbers?" which the obvious answer is "no" because numbers go on forever. originally posted by irichc: "Can any mathematician picture infinity?" Yes! Calculus has an uncanny way of explaining things that would otherwise be very difficult to understand. The hard-to-grasp concept of infinity is one of these specialties that Calculus (specifically Differential and Integral) is irreplaceable in explaining. Many things increase at different rates (sometimes constantly and without end, like infinity) which can be described by Functions. Many of Calculus's functions have Limits (a very important part of Calculus) that surpass boundaries beyond logic! This means that the domains and ranges cannot be contained in numbers that we can work with, because the numbers keep getting larger (they do not stop, like infinity). But this functional problem is easily taken care of by the use of infinite limits (divergence), even though the limits cannot exist AT infinity. Yet each of these functions of growth has some factor that allows it to grow only so much. These concepts can be drawn on a graph. Graphically speaking, limits involving infinity result from functions that have horizontal, and/or vertical, asymptotes. An asymptote is a value in the domain or range that the function is not defined at (most often to avoid division by zero). Horizontal asymptotes occur at restricted y - values, and vertical asymptotes occur at restricted x- values. This creates a graph that approaches these asymptotes but never actually touches them. As the values of x approach vertical asymptote(s) the values of y tend toward +/- infinity. When a function has horizontal asymptote(s) the y � values approach the asymptote as the x � value approach +/� infinity. The properties for limits as x---> +/� infinity can be applied to higher order polynomials, and rational functions. If a rational function can be reduced, then the properties may be applied to it in order to find the limit. The function is reduced by dividing each element by the highest power of x in the denominator. The reason for this is to create a function that contains a constant and multiples of 1/x in the denominator. Once the function is of this form we know the limits of each term and may apply the properties of limits. An infinite limit describes the limit of a function that keeps growing as x approaches a given value. The two main occurrences of infinite limits are: 1) The limit as x approaches the value of a vertical asymptote, the value of the function is always growing. 2) Any polynomial of degree 1 or greater. (This includes simple functions of the form f(x) NOT rational functions of the form f(x)/g(x)). These polynomials will eventually take off to infinity. Which gives them a limit of +/-infinity as x---> +/-infinity. What happens when the degree of the numerator exceeds the degree of the denominator is that the limit goes to infinity. To find the limit as x---> +/-infinity of a rational function compare the degree of the numerator and denominator: a) same degree: the limit equals the ratio of the coefficients of the highest order terms. b) numerator of lower degree: the limit equals 0, because all of the terms in the numerator will be multiples of 1/x, and the limit of the numerator will be 0. c) numerator of higher degree: the limit will approach +/-infinity. The direction of the limit will depend on the interaction of the signs in the numerator and denominator as x---> +/-infinity. When we deal with the limits of quantities, very often we have to compare numbers such as: adding two large numbers (they can be infinite); multiplying two large numbers; subtracting two large numbers; multiplying a large number with a small number; Though it is easy to check that adding two large numbers is a large number (that is infinity+infinity=infinity), it is absolutely not clear what happened if we subtract a large number from another large number. We say that we have an indeterminate form. May be one of the most important indeterminate form is the quotient of two small (or large) numbers. Infinite Limits for Rational Functions, Divergence, Vector Spaces, Infinite Intervals...these only scratch the surface of what Calculus can do.

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