Stupid Math Tricks

drawmack

infinity - any finite number = infinity, but is it a little bit less infinity?

1/3 = .33

1/3 + 1/3 + 1/3 = 1
.33 + .33 + .33 = .99
.99 = 1

2³ = 2 2 2 = 8
2² = 2 2 = 4
2¹ = 2 = 2
2 ⁰ = * = 1

Moonglobe

lol and your point?

Weedpacket

Er, which infinity are you talking about? omega? Aleph-null? C? ...?

Hey, I'm a mathematician. I have to worry about these things.

BuzzLY

That's not a stupid math trick. This is a stupid math trick:

You and two friends share a motel room. The rate is $30, so you each give $10 and settle in for the night. The manager realizes he overcharged you, and orders the bellhop to return $5 to you. He does so, and for his trouble, you decide to tip him $2, and return one dollar to each of you.

In essense, the three of you each paid $9 for the room ($10 minus the one you got back), totalling $27, and gave the bellhop $2, for a grand total of $29. What happened to the other dollar?

Weed, don't you dare answer this one... :p

jstarkey

Whoa, I've been telling that one for 17 years. I still keep forgetting the answer.

[edit]

Ahhhhhh, now I remember. Can I tell, can I tell?

BuzzLY

Aw... let's let it percolate a bit... although I'm sure there're quite a few people here that know this one. At least wait until the morning, when people have had time to answer... or hide your answer 😉

Hell... you're the admin. Do whatcha want :rolleyes: 😃

piersk

<-- 😕

drawmack

Originally posted by BuzzLY
In essense, the three of you each paid $9 for the room ($10 minus the one you got back), totalling $27, and gave the bellhop $2, for a grand total of $29. What happened to the other dollar?

This is a rounding error as demonstrated in my first post 1/3 = .33

Each person antied up $10 for a total of $30

They were susequently refunded $5 for a total of $25

Meaning that each person paid 10 - (5/3) dollars for the room

This comes out to two of the people paying $8.33 and one person paying $8.34.

They each gave the bellhop a tip of 2/3, or one person tipping $0.66 and two people person tipping $0.67.

And taking back $1.00 each for a total of $3.00

Now when we total all that up:
8.37
8.33
8.33
0.66
0.67
0.67
3.00

we get $30.00

Any programmer who cannot answer a problem that deals with rounding errors is in trouble and had better not be writting software for my bank.

Now the real question is this, why can't a computer exactly represent the value 0.1 in binary?

piersk

Originally posted by drawmack
Now the real question is this, why can't a computer exactly represent the value 0.1 in binary?

Who said it couldn't?

Merve

And thought I was the only one obsessed with math and PHP!

Look here...

Can you believe I spent practically my whole summer on that?

BuzzLY

I suppose that's one way to look at it, drawmack. The other way is to realize that I counted the bellhop's tip twice. The fact is, you paid $27 for the room. $25 of that went toward the price of the room, and $2 went to the bellhop. If you all paid $30, then you each get back $1. Simple as that. You don't have to figure fractions at all. 🙂

drawmack

that's still messed up Buzz, if you counted the bell hop's tip twice you should have come out to $28 not $29

drawmack

Originally posted by piersk
Who said it couldn't?

Binary cannot represent 0.1 so they have come up with a standard that makes all computers lie the same way. But the standard does not change the fact that 0.1 cannot be represented in binary.

BuzzLY

Nope.

Room: $25
Tip: $2
Subtotal: $27 (and incidentally, $9 per person for the room AND tip) 😉
Tip: $2 (second time counted)

Total: $29

Proving that I was right all along: Priceless 😃

drawmack

okay so you double count the tip and don't count the $3.00 the people got back, I get get it now. Neat

piersk

Originally posted by drawmack
Binary cannot represent 0.1 so they have come up with a standard that makes all computers lie the same way. But the standard does not change the fact that 0.1 cannot be represented in binary.

IEEE 745 is a representation of a decimal number. It means that computers can represent floating point numbers in binary.

Weedpacket

Originally posted by piersk
IEEE 745 is a representation of a decimal number. It means that computers can represent floating point numbers in binary.

But decimal is itself a format for representing numbers. So is binary.

The binary representation of one-tenth doesn't terminate (i.e., can't be representated by a finite sum of terms of the form 2^-n where all the ns are different positive integers) in the same way that the decimal representation of one-seventh doesn't (i.e., can't be represented by a finite sum of terms of the form 10^-n where all the ns are different.)

One-tenth in binary is 0.001100110011.... Multiply that by 1010 and you get 0.1111111.... = 1.000000.......

piersk

Originally posted by Weedpacket
But decimal is itself a format for representing numbers. So is binary.

Thats what I was implying.