64 bit support on iMac Core 2 Duo under Tiger 10.4.10 ?

Hi,
everywhere I read that my iMac Core 2 Duo is supposed to support 64bit applications, or it least is "64bit ready". What does this precisely mean for Tiger? I am running 10.4.10.
The concrete problem I have is that Mathematica 6 is supposedly supporting 64bit on Intel, one just needs to rename the Kernel; a 64 bit Kernel is included. See http://support.wolfram.com/mathematica/systems/macintosh/osx/32bitratherthan64bi t.html
However, it does not even run on the command line, where it gives an error:
iMac.local:MacOS => MathKernel64
tcsh: MathKernel64: Bad CPU type in executable.
lipo tells me:
iMac.local:MacOS => lipo -detailed_info MathKernel64
input file MathKernel64 is not a fat file
Non-fat file: MathKernel64 is architecture: x86_64
On the other hand, the architecture of the other running apps is i386.
I gather that architecture x86_64 is not supported on my iMac?
The makers of Mathematica, on the other hand, clearly say that it should run on my Core 2 Duo iMac under 10.4.10.
So I am confused; do I have to wait for Leopard?

Yes, this thread is older and newer....
Parts of Mac OS X 10.4 Tiger are 64-bit, and parts are not.
Per published information, a whole lot more of the Mac OS X environment is going to 64-bit; Tiger had 64-bit at the Unix level, while Leopard is expected to bring rather more to the table.
Published high-level details:
http://www.apple.com/macosx/leopard/technology/64bit.html
http://developer.apple.com/leopard/overview/
For low-level details and such related to Leopard, those are under NDA up until they're not under NDA. Mayhap clarification arrives sometime next month?
The x86-64 construct is a name for what Intel once called its EM64T extensions and what it now (in aggregate) refers to as its Intel 64 architecture. Not to be confused with IA-64, which is Itanium, nor with IA-32 which is the 32-bit x86 stuff; x86-32. AMD64 is what AMD has called its extensions, and these are compatible with Intel 64.
Yes, the Intel Core 2 processors and the Intel Xeon 5100 series processors can and do have 64-bit addressing support. But there's a whole lot more to this than the processor itself, as assumptions of the address size tend to permeate an operating system and interfaces and applications; APIs and data structures are notorious for harboring these assumptions. Run-time code can and does tend to make pointer size assumptions here, too.
"64-bit Ready" means that once the software and applications get around to it, the hardware is expected to be ready. It doesn't mean that it'll all work together flawlessly, unfortunately.
Since the makers of Mathematica have provided the bits here and it is the Mathematica bits that are reporting errors, I'd have to assume they're the best ones to look at this. Check with Mathematica.

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Why reward points?(Quoted from Discussions Terms of Use.)
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Members may reward you with 5 points if they deem that your reply is helpful and 10 points if you post a solution to their issue. Likewise, when you mark a reply as Helpful or Solved in your own created topic, you will be awarding the respondent with the same point values.

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thank you

thank you for that.....this help me decide eother to purchase 2gb stick or not....well i heard from some website said that when apple post the specification at that time 2 gb stick still not b on the market just yet.....
http://en.wikipedia.org/wiki/Macbook
said that late 2006 macbook is able to put 4 GB too but only 3.25 readable.....while the other ram site that selling ram for mac product also state this point i'm not pretty sure about that......
i get pretty clear that for macbook late 2006 able to run with 3 gb even though apple specification said only 2gb.....
since imac core 2 duo 1.83Ghz is not an official imac standard...is for education.....so it hard to find the information......
i really want to get the info of who experience or have try on t it.....
but thank for your kind...that comment this post ir really helpfu for me too

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iMac Core 2 Duo, 3.06 GHz, 8 GB RAM, early 2009.

CRASH REPORT:
Process:         Aperture [667]
Path:            /Applications/Aperture.app/Contents/MacOS/Aperture
Identifier:      com.apple.Aperture
Version:         3.2 (3.2)
Build Info:      Aperture-201088000000000~1
App Item ID:     408981426
App External ID: 4372644
Code Type:       X86-64 (Native)
Parent Process: launchd [130]
Date/Time:       2011-10-20 21:23:47.680 +0200
OS Version:      Mac OS X 10.7.2 (11C74)
Report Version: 9
Interval Since Last Report:          77957 sec
Crashes Since Last Report:           53
Per-App Interval Since Last Report: 206 sec
Per-App Crashes Since Last Report:   52
Crashed Thread: 0 Dispatch queue: com.apple.main-thread
Exception Type: EXC_BAD_ACCESS (SIGSEGV)
Exception Codes: KERN_INVALID_ADDRESS at 0x0000000000000000
VM Regions Near 0:
-->
    __TEXT                 0000000100000000-000000010078c000 [ 7728K] r-x/rwx SM=COW /Applications/Aperture.app/Contents/MacOS/Aperture
Application Specific Information:
objc[667]: garbage collection is OFF

64 bit support on iMac Core 2 Duo under Tiger 10.4.10 ?

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