Nerd challenge: make 100 < 99

[darkyam]

How many ways can you find to make 100 < 99 by adding just one symbol to both? Here are the rules:
1. The same symbol has to be added to both sides in the same place. If a symbol is added between the 1 and first 0, it has to be added before the first 9. Any math involved assumes a 0 is before the 9, so that 1*00 = 0*99 and is thus not a valid answer.
2. Any math that returns an error in Excel is not allowed, so 10/0 doesn't make it less than 9/9.
3. If the symbol is not recognized in Excel, it has to be relatively commonly seen in the real world.
4. Symbols only, no numbers or letters.
5. Formulas need to evaluate the numbers separately, if done in Excel. Using < between the numbers, as mewingkitty has cleverly found out below can make 100 evaluate to 1 and 99 to 0, but still prove true.

I have ten such ways so far. I don't know if it's possible, but I'd like to shoot for 20.
1. Putting a bar over both numbers, like you would see under the six and nine on billiard balls, thus turning both numbers over.
2. The obvious one: -100 and -99
3. 1:00 and :99
4. 10^0 and 9^9
5. 10*0 and 9*9
6. 1+00 and 0+99
7. 10+0 and 9+9
8. 10√0 and 9√9
9. 1√00 and √99
10. 10=0 and 9=9, which evaluate to False (0) and True (1).

*Edit: Just realized one of mine, #9 doesn't work, since it assumes you're multiplying the square root of 99 by a leading 0. Back down to nine ways.

[teylyn]

1010 and 919 (read 1010 as binary, =BIN2DEC(1010) equals 10, and 910 as decimal ) Would that count? If so, then also

1100 and 199

[darkyam]

I'm not quite sure I follow what symbol you're adding to get the binary to 1010 and 910. Could you please elaborate your steps a little bit?
The object is to do this all in one step with just one symbol. If there's a symbol for making something binary that could be inserted between the numbers, that could potentially count.
At the very least, bringing binary into it is a clever attempt, even if it doesn't end up working out.

[mewingkitty]

=.100<.99
=1&00<9&9
=10>0<9>9

mew?

Is this according to Excel or according to reality? :P

[darkyam]

Nice try, but I'm not sure I agree with that one. -100 is less than -099, but .100 is still greater than .099. The leading 0 is proving to be a pain in the butt, isn't it?

Well done on the second one. We have ten ways now. Perhaps 12, once I understand Teylyn's response better.

Sorry last one I posted shoulda read: =10>0<9>9

Interesting. It works in Excel, but only because Excel reads from left to right. Breaking it up into two separate formulas, though, it doesn't work because 10>0 evaluates to True while 9>9 is False, so it's still 1 to 0. Hmmm...I'll have to think about it before I make a ruling on that one. Very clever, though.

*Edit: Thought about it, but couldn't get over the fact that 10>0 evaluates to 1 and 9>9 is 0. I have changed the rules above and given you credit for the find.

[teylyn]

I'm not quite sure I follow what symbol you're adding to get the binary to 1010 and 910. Could you please elaborate your steps a little bit?

Sorry, I had a typo, which I corrected since then. I'm adding a 1

100 < 99

becomes

1010 and 919

Everything else is just interpretation. So if I interpret 1010 as a binary, it will be less than the decimal 919

[darkyam]

Ah, I get it now. But rule 4 says you can only add symbols. Also, what you do to one must be done to the other, so if one becomes binary, both must be.

[darkyam]

Got one more, courtesy of a friend of mine: 1<00 and 0<99.

[teylyn]

how does that work then?

1<00 = False and 0<99 = True

so

False < True

coerced into

0 < 1

Is that it?

[darkyam]

Yep, just like #10 in my original post.

[pike]

sin(100-9)<sin(99-9)

[scaffdog845]

=10^0<09^9 ....... ops. overlooked this in original post. Nevermind

[darkyam]

Pike, you've added both letters and numbers to each side. Rule #4 disallows this. If there's a single symbol to do what you've done, though...

[ChemistB]

How about
~100<~99?
This certainly has the possibility of being true especially as we do not know the # of significant digits in 100

[darkyam]

ChemistB, could you please elaborate? I'm not familiar with the function of ~. The uses I've seen of it mean "approximately". If we're using it like that (as a form of rounding), then I think we'd have to assume the same level of rounding for each number, to keep the changes to both sides even. Is there another use for it?

[ChemistB]

No I am using it as approximate. Often approximate is used with a specific range (e.g. 100 +/- 5). You could say you have approximately $100 in the bank while I have approximately $99 in the bank. I might have more than you.

[darkyam]

Well, you might, but that doesn't make 100<99 as much as raises a doubtful possibility that it could be. If we were to use it as approximately in the same sense of each (i.e., with the same error range), then the assumption is that an average of a sample of values within the error range would come out to 100 and 99, give or take. It's a nice try, but without a definite proof, I'm going to have to disallow it.

[pike]

struth.. looks like I failed the nerd test.. I was a bit worried for a while

[Unnamed Narrator]

2. Any math that returns an error in Excel is not allowed, so 10/0 doesn't make it less than 9/9.

The fact that this returns an error is not the only reason 10/0 isn't less than 9/9.

10/0 tends to infinity while 9/9 = 1

[xladept]

100 mod 2 < 99 mod 2