http://www.chabad.org/library/article_cdo/aid/2830/jewish/What-Is-Sin.htmLike almost everything else, it depends on who you ask.
The Midrash (Yalkut Shimoni on Psalms 25) describes a sort of "panel discussion" in which this question is posed to four different authorities -- Wisdom, Prophecy, Torah and G-d -- each of whom gives a different definition of sin.
According to Wisdom sin is a harmful deed. According to Prophecy it is death. Torah sees it as folly. And G-d sees it as an opportunity.
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"Prophecy" takes this a step further. Sin is not only a harmful deed -- it is the ultimately harmful deed. Prophecy (which represents the apogee of man's endeavor to commune with G-d) defines "life" as connection with G-d. Sin--man's turning away from G-d--is a disruption of this connection. Hence, sin is death.
http://www.torah.org/learning/haftorah/parah.html.
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Yechezkel's analogy suggests a direct corollary between sin and death. Apparently, the ultimate removal of sin is similar to the removal of the impurity of death.
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From Daf Yomi Shabbat 55
2) IS THERE DEATH WITHOUT SIN?(a) (R. Ami): One does not die without Chet - "Ha'Nefesh ha'Choteis Hi Samus?";
1. One is not afflicted (Tosfos - severely) without Avon (intentional sin) - "U'Fokadti v'Shevet Pish'am uvi'Nga'im Avonam".
55b-------------55b
(b) Question (Beraisa #1): The angels asked Hash-m why he decreed death on Adam ha'Rishon. (Mahadurah Basra - many Mitzvos involve death, surely there would be death even had Adam not sinned - why is death attributed to his sin?)
1. Hash-m: I gave one easy Mitzvah to him, and he transgressed it!
2. The angels: Moshe and Aharon fulfilled the entire Torah, yet they died! (They thought that Hash-m answered why Adam died.)
3. Hash-m: "Mikreh Echad la'Tzadik vela'Rasha" (I decreed that all people will die.
Indeed, Moshe and Aharon sinned at Mei Merivah, but this did not cause their death, it only forbade them to enter Eretz Yisrael.)(c) Answer: R. Ami holds like the following Tana:
1. (Beraisa #2 - R. Shimon ben Elazar):
Even Moshe and Aharon died on account of their sin - "Ya'an Lo He'emantem Bi" - had you trusted Me [to speak to the rock exactly as commanded; alternatively, had you done so, you would have elevated Benei Yisrael's belief in Me, and] you would not have to die now.(d) Question (Beraisa #3): Four people died only on account of [Adam's sin through] the snake (Me'iri - their sins were so small, one cannot fathom that they should be judged for them) - Binyamin, Amram, Yishai, and David's son Kalev.
1. Question: It says "Avigayil Bas Nachash Achos Tzeruyah" - [this] Avigayil was the daughter of Yishai, not of Nachash!
2. Answer: Yishai is called Nachash to teach that he died only on account of the snake.
3. We have a tradition about the other three.
4. Question: Who is the Tana of Beraisa #3?
i. It is not Tana #1 - he holds that Moshe and Aharon also died without sin!
5. Answer: It is R. Shimon ben Elazar - even he holds that one can die without sin and [presumably, also] one may be punished without Avon.
(e) R. Ami is refuted.
PS: It does appear that your opinion is supported in this Daf Yomi on Shabbat 55, but there is another opinion...