According to a website I found this morning, 0.999… is the same as 1. Not just very close, but precisely identical:I'm definitely one of those people who find it deeply counterintuitive. Can anyone explain this in layman's terms?
*edit: upon further examination, it seems the only reason this holds up is because when you multiply by 10 to get 9.999..., you effectively have just added one more 9 to the already infinite number you had before... That's hard to wrap your mind around. If you place a limit on infinity then this proof wouldn't work.
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- Luke
- I started this blog out of curiousity and it grew to become a great encouragement for me in my Christian walk. I hope the writings here can be used by God to further His work in your life.
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10 comments:
while the proof is interesting, it obviously won't work. It is impossible to take 10-.9999... and equal 9. it will always be 10.00...1. An interesting play on mathematics though.
Brett: I'm confused...at what point did we take 10 - .999...?
We do take 10 and multiply by .999... which gives us 9.999... and then we subtract .999...
Are you saying it's impossible to subtract .999... from 9.999...?
If that's what you're saying, why is it impossible?
Your right, I missed the multiplying by .999...
so, the problem is not quite as obvious as my little error made it. You're correct. It is much more difficult to picture. Wow! Thanks for correcting me.
in layman's terms (according to my calc 2 teacher)... can you think of any number that would be between 0.999 repeating and 1? I can't.
Therefore, 0.999 repeating is essentially 1.
:)
Another way to get a gut understanding of this is that 1/3 + 1/3 + 1/3 = 1 and 1/3 = .333...
So 1/3 + 1/3 + 1/3 = .999... which is the same as 1.
Because .999... goes on forever, it is infinitely close to 1, and it is equal to 1.
So, if the creation contains deeply counterintuitive truths, what does that tell us about the Creator?
Matthew: Yeah, I ran across that proof too. It uses the "if a=b and if a=c then b=c" logic.
Don Pelon: What does it tell you?
Not allowed to answer a question with a question. (Even though Jesus did.)
So, (in spite of my indignation) .. it tells me that He wasn't kidding when He said the wisdom of men is foolishness with God. I don't think he's equipped our brains with enough processing power to comprehend the fullness of knowledge and wisdom. It also challenges me to know Him better through understanding His handiwork to the best of my ability.
Your turn.
D.P.: Ro 11:33
O the depth of the riches both of the wisdom and knowledge of God! how unsearchable are his judgments, and his ways past finding out!
I love the fact that there are exclamation points in there. :-)
I also love how He saw fit to give us inquisitive minds, so that we would wonder about stuff like this. Then, the more we learn, the more we uncover, the more we find we really don't have a clue what holds it all together.
Big God, Little me
Amen.
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