Specifically, it marks the beginning of the siege around Jerusalem by the Babylonians, prior to the destruction of the first Beit HaMikdash. It thus commemorates the beginning of the Churban.
To the 10th of Tevet has been added events that are associated with the 8th of Tevet - namely, the "tragedy of the Targum Shiv'im", the first (and coerced) translation of the Torah into Greek. The day is considered as "dark" as the day of the Sin of the Golden Calf. Literal translation of the Written Torah without the inseparableOral Law, opens the Torah to misunderstanding and distortion, the effects of which have haunted us throughout the generations; And the 9th of Tevet - namely, the anniversaries of the deaths of Ezra and Nechemia, who represent for us the restoration of Torah study and practice after a long spiritual drought, and the return (albeit in disappointingly small numbers) of the Jews to Eretz Yisrael from exile.
In our time, an additional element was added to Asara b'Tevet - namely, it has been declared as Yom Kaddish K'lali - a day of saying Kaddish and remembering victims of the Holocaust whose actual dates of death will remain forever unknown to their families and all of Israel.
A major minor
WRONG! It is clear in the sources of Jewish law that a healthy person - male and female, adult and child from 13/12 years of age - is REQUIRED to fast on Asara b'Tevet (and the other fasts). True, there are several "types" of individuals that are exempt from fasting. Many authorities exempt from fasting pregnant women,nursing mothers, people with various and sundry medical conditions that can worsen as a result of a fast, frail people. If a person suspects that he/she should not fast, a Rav should be consulted. But healthy people - even those weakened by fasting, but not unusually so, MUST fast. It's as simple as that. Do not be misleadby commonly held misconceptions.
In addition to the non-fasting types mentioned in the previous paragraph, there are other leniencies that apply to Asara b'Tevet, that should be accepted for what they are, and not taken as indicators to ignore the Fast. For certain reasons, the Sages allowed us to begin the fast at dawn, instead of prior to sunset the evening before. They also did not "impose" upon us the "additional" restrictions of Yom Kippur and Tish'a b'Av.
Only eating and drinking is forbidden on Asara b'Tevet; washing, use of lotions etc., wearing of leather shoes, and marital relations are not forbidden.
These leniencies notwithstanding, the Shulchan Aruch states clearly that a healthy person who will not be harmed by the fast, MUST fast on the required days.
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