0.9999999999... = 1?

Posted on December 6, 2005 by timlyg

This excerpt from Danica McKellar's site:

Danica Answers: Hi Tom! Glad to help- you're not the only one who's asked me to repeat this. 🙂

First, we start by labeling:

x= .999999999999..... (repeating infinitely)

Then if you multiply both sides by 10, you get:

10x = 9.99999999999..... (repeating infinitely)

Well,
what if we subtracted the top equation from the bottom one? We'll get
another true statement. Before I do that, let me review why this will
work. Say that a = b , and c = d. Then do you agree that "a-c = b-d" is
also a true statement? After all, a = b , and c = d. So once you agree
with that, let's continue and go ahead and subtract the top statement
from the bottom one. We get, for the left hand side of the equations:

10x -x = 9x

And for the right hand side:

9.99999..... - .99999999...... = 9

And
we conclude that "9x = 9" is also a "true statement." Divide both sides
by 9, and you get x = 1. Since we started with x = .9999999 (repeating
infinitely), we've now shown that the "infinite decimal of .9999
repeating" equals the whole number 1. Yes, I did it much faster on the
TV show. 🙂

What
I didn't talk about on the show is the somewhat philosophical issue
this proof brings to light. Our mathematical system was invented by the
human mind, which assumes that space (and the number line) is
infinitely divisible and that there *is* such thing as a theoretical
"point" that takes up no space, and has no volume or mass. So, this
little proof shows that - according to a math system that assumes such
things - indeed, .999999.... (repeating infinitely) equals 1. There are
those who would say this isn't true, but then they are forgetting that
we are dealing with a "language" that was invented by the human mind,
and also that infinity is a slippery concept. 🙂

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The dilemma to this problem is indeed infinity itself.

Don't forget, 10x is actually 10 * 0.99999999.... hence, if we treat infinity as we treat regular numbers which are calculated from one end to another end of the decimal, we have to treat the calculation as such:

10 * 0.9999... would have to have resulted a "0" at the right end of the infinite 9.99999999...."0".

Thus, 10x - x = 9x would not have made 9x = 9. But actually 8.999999999...."1".

I agree with Danica that this is the flaw of human terminology, but I wouldn't give up on the terminology of infinity just so easily.

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Sleep

Posted on December 6, 2005 by timlyg

I have come to realized that I am occupying my time with so many things that I have forgotten to schedule a time for sleep.

Sleep cannot simply be dismissed, or I wouldn't have the right brain cells to work out the next wake's journey.

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ThanksGiving Remark...Superstition, Sleep Paralysis.

Posted on December 6, 2005 by timlyg

It was remarkable how we humans thought when something beyond our comprehension is happening to us. We would try to have our own creative ideas, and assumption...especially when we thought no one else could have experienced such things. And when that assumption becomes absolute, we come to a point where fools are.

Such is superstition.

Nevertheless, there are times when it is revealed to us the things beyond our comprehension. The source of such revelation is often questioned. And when it comes to God, this has to do with faith.

Last Thursday I witnessed a brother giving a testimony on what he claimed to be demonic possession in which every symptoms described are that of sleep paralysis, or hypnopompic/hypnagogic.

From the Bible, demonic possession is very real, despite of what many in today's era believing it to be a form of mental illness.

I believe that due to superstitions, we gave the real demons the ability to take control, and eventually, possessing a person. Of couse, this is just one of many ways for such demonic entrance.

However, we cannot ignore the truth. At the dawn of science, evolution and psychology, we christians were suffering multiple attacks and couldn't react, making ourselves scorned by many of the "educated".

I have come to hear more than one testimony nowadays which aren't witnessing Christ, glorifying our Lord. These testimonies bore title of Christ but contents of self-honor, self-dignity, self-glorification and of the things that are false, of the things that satisfy the itching ears.

Those who heed reasons, may not come to the Lord.
Those who ignore reasons, wouldn't come to the real Truth.

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Posted in General | 1 Comment

Yawning

Posted on December 6, 2005 by timlyg

I wonder of the true mystery of yawning...

It seems many understood it as only a sign of emotional stress.

I wonder, has it ever been widely considered as relief? It has often been the case in my life. So why would one truely yawn...How is voluntary yawn conducted?

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Tired...

Posted on December 3, 2005 by timlyg

Very tired. Got Sunday School material to prepare for. Looks like it's another long night. I'll vacuun the carpet tomorrow.[@more@]

Posted in General | Leave a comment

Personality & Pets

Posted on December 3, 2005 by timlyg

How is it that a person can be judged by his/her pet(s)?

I believe psychologically, there are a few categories which reflect a person's few characteristic:

1. No pets: either extremely friendly or perhaps just the opposite.

2. Types of pets. Sizes of pets.

3. Number of pet(s) vs size of human family living together.

4. Attitude towards pet(s) vs attitude towards any human.

The difference between humans and pets is a qualitative difference. So if you like children, please don't replace such notion with pets.

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Computer Problem

Posted on December 2, 2005 by timlyg

A 650Watt Power Supply has resolved certain problem, from a 425Watt.

However, it seems to be temporary. Somehow, I think upgrading the power supply may have been merely adding wings to a car.

It comes to this, problem is either with the video card, or the motherboard.

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Jesus & Judas

Posted on December 1, 2005 by timlyg

Jesus seems harsher to Peter than to Judas...why?

Could it have anything to do with Philippians Chapter 1? verses 15 onwards?

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Contradictory vs Paradoxical

Posted on November 29, 2005 by timlyg

Many, especially ones in business dealings, face contradictory matters each day. Therefore, they are susceptible to presuming paradoxical contents of the Bible as contradictory. Hence, if they were christians, they would either be troubled by such matter, or dissevering the Word of God as if separating a limb from the rest of the body.

Posted in Theologization | 1 Comment

Rebuke

Posted on November 28, 2005 by timlyg

I realized today that if one rebukes with the fear of the Lord, one is in God's favor. But, but...when one rebukes in such a way, one must be bold to go all the way.

In addition to this experience, I would like to add a good verse under KJV and Chinese's HeHeBen Translation:
Surely the wrath of man shall praise thee: the remainder of wrath shalt thou restrain. (Psalms 76:10)

人的忿怒要成全你的榮美；人的餘怒，你要禁止。

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